{"id":1600,"date":"2026-03-16T20:23:29","date_gmt":"2026-03-16T19:23:29","guid":{"rendered":"https:\/\/blog.phiboard.com\/?p=1600"},"modified":"2026-03-28T16:45:54","modified_gmt":"2026-03-28T15:45:54","slug":"liczby-naturalne-czesc-1","status":"publish","type":"post","link":"https:\/\/blog.phiboard.com\/en\/liczby-naturalne-czesc-1\/","title":{"rendered":"Natural numbers \u2013 Part 1"},"content":{"rendered":"<div data-elementor-type=\"wp-post\" data-elementor-id=\"1600\" class=\"elementor elementor-1600\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ae28d82 e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-parent\" data-id=\"ae28d82\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-c1c428e e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"c1c428e\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1a508ed elementor-widget elementor-widget-hfe-breadcrumbs-widget\" data-id=\"1a508ed\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"hfe-breadcrumbs-widget.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<nav aria-label=\"Breadcrumb\"><ul class=\"hfe-breadcrumbs\"><\/ul><\/nav>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-8f310ee e-con-full card e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"8f310ee\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t<div class=\"elementor-element elementor-element-92599e2 e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"92599e2\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-8a59131 elementor-widget elementor-widget-wpr-post-media\" data-id=\"8a59131\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"wpr-post-media.default\">\n\t\t\t\t\t<div class=\"wpr-featured-media-wrap\" data-caption=\"standard\"><div class=\"wpr-featured-media-image\" data-src=\"https:\/\/blog.phiboard.com\/wp-content\/uploads\/2026\/03\/Projekt-bez-nazwy79.png\"><img decoding=\"async\" src=\"https:\/\/blog.phiboard.com\/wp-content\/uploads\/2026\/03\/Projekt-bez-nazwy79.png\" alt=\"\"><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0f2c006 elementor-widget elementor-widget-page-title\" data-id=\"0f2c006\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;align_tablet&quot;:&quot;left&quot;}\" data-widget_type=\"page-title.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\n\t\t<div class=\"hfe-page-title hfe-page-title-wrapper elementor-widget-heading\">\n\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/blog.phiboard.com\/en\">\n\t\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-xl\">\n\t\t\t\t\t\t\t\t\n\t\t\t\tNatural numbers \u2013 Part 1  \n\t\t\t<\/h2> \n\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-34e0e19 elementor-widget elementor-widget-text-editor\" data-id=\"34e0e19\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Hi.<\/p>\n<p>I believe that the best way to learn mathematics is by solving problems. Calculating, calculating, and calculating again\u2014starting with the simplest exercises, learning the basic patterns, and gradually progressing to more difficult ones.<\/p>\n<p>In connection with this, I decided to create a place where at least one problem will appear every day. Each problem will be solved and explained step by step, showing where everything comes from and what follows, as well as what you need to know to solve it on your own.<\/p>\n<p>However, dear reader, I encourage you to first try solving the problems on your own, and only if you encounter difficulties, then use the solution and the explanation.<\/p>\n<p>Each problem will be available for download as a PDF file.<\/p>\n<p><\/p>\n<p>I wish you productive studying \ud83d\ude42<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0560119 elementor-widget elementor-widget-heading\" data-id=\"0560119\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">So, let's get started \ud83d\ude42<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8aa2ce7 elementor-widget elementor-widget-text-editor\" data-id=\"8aa2ce7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Today, we will start with natural numbers.\u00a0<\/p>\n<p>Let's consider how to calculate how many natural numbers are less than a given number and divisible by a specific number.\u00a0<\/p>\n<p>The problem is below. Take a look \ud83d\ude42<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-acbd820 elementor-widget elementor-widget-shortcode\" data-id=\"acbd820\" data-element_type=\"widget\" data-e-type=\"widget\" data-no-translation=\"\" data-widget_type=\"shortcode.default\">\n\t\t\t\t\t<style>.elementor-element-acbd820{display:none !important}<\/style>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6724f9b elementor-widget elementor-widget-shortcode\" data-id=\"6724f9b\" data-element_type=\"widget\" data-e-type=\"widget\" data-no-translation=\"\" data-widget_type=\"shortcode.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-shortcode\"><a href=\"https:\/\/blog.phiboard.com\/wp-content\/uploads\/2026\/03\/exercise1.pdf\" class=\"pdfemb-viewer\" style=\"\" data-width=\"max\" data-height=\"max\" data-toolbar=\"bottom\" data-toolbar-fixed=\"off\">exercise1<\/a><\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-238b2d9 elementor-widget elementor-widget-button\" data-id=\"238b2d9\" data-element_type=\"widget\" data-e-type=\"widget\" data-no-translation=\"\" data-widget_type=\"button.default\">\n\t\t\t\t\t<style>.elementor-element-238b2d9{display:none !important}<\/style>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-790d28b elementor-widget elementor-widget-button\" data-id=\"790d28b\" data-element_type=\"widget\" data-e-type=\"widget\" data-no-translation=\"\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/blog.phiboard.com\/wp-content\/uploads\/2026\/03\/exercise1.pdf\" target=\"_blank\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Download the PDF file<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-8d3edbf e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"8d3edbf\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-6e6b0a4 e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"6e6b0a4\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-37e1a07 elementor-widget elementor-widget-text-editor\" data-id=\"37e1a07\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Share this post<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-df68b2d elementor-grid-0 elementor-widget elementor-widget-wpr-sharing-buttons\" data-id=\"df68b2d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"wpr-sharing-buttons.default\">\n\t\t\t\t\t<div class=\"wpr-sharing-buttons elementor-grid wpr-sharing-official wpr-sharing-label-off wpr-sharing-label-tr\"><div class=\"elementor-grid-item\"><a href=\"https:\/\/www.facebook.com\/sharer.php?u=https:\/\/blog.phiboard.com\/en\/liczby-naturalne-czesc-1\/\" class=\"wpr-sharing-icon wpr-sharing-facebook-f\" title=\"\" target=\"_blank\"><i class=\"fab fa-facebook-f\"><\/i><\/a><\/div><div class=\"elementor-grid-item\"><a href=\"https:\/\/twitter.com\/intent\/tweet?url=https:\/\/blog.phiboard.com\/en\/liczby-naturalne-czesc-1\/\" class=\"wpr-sharing-icon wpr-sharing-twitter\" title=\"\" target=\"_blank\"><i class=\"fab fa-twitter\"><\/i><\/a><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-c2343f3 e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"c2343f3\" data-element_type=\"container\" data-e-type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2aa28a3 elementor-position-top elementor-widget elementor-widget-image-box\" data-id=\"2aa28a3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image-box.default\">\n\t\t\t\t\t<div class=\"elementor-image-box-wrapper\"><figure class=\"elementor-image-box-img\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1430\" height=\"1430\" src=\"https:\/\/blog.phiboard.com\/wp-content\/uploads\/2026\/02\/574329864_122147990048826970_4282488714973042999_n-e1771362224679.jpg\" class=\"attachment-full size-full wp-image-873\" alt=\"\" srcset=\"https:\/\/blog.phiboard.com\/wp-content\/uploads\/2026\/02\/574329864_122147990048826970_4282488714973042999_n-e1771362224679.jpg 1430w, https:\/\/blog.phiboard.com\/wp-content\/uploads\/2026\/02\/574329864_122147990048826970_4282488714973042999_n-e1771362224679-300x300.jpg 300w, https:\/\/blog.phiboard.com\/wp-content\/uploads\/2026\/02\/574329864_122147990048826970_4282488714973042999_n-e1771362224679-1024x1024.jpg 1024w, https:\/\/blog.phiboard.com\/wp-content\/uploads\/2026\/02\/574329864_122147990048826970_4282488714973042999_n-e1771362224679-150x150.jpg 150w, https:\/\/blog.phiboard.com\/wp-content\/uploads\/2026\/02\/574329864_122147990048826970_4282488714973042999_n-e1771362224679-768x768.jpg 768w, https:\/\/blog.phiboard.com\/wp-content\/uploads\/2026\/02\/574329864_122147990048826970_4282488714973042999_n-e1771362224679-12x12.jpg 12w\" sizes=\"(max-width: 1430px) 100vw, 1430px\" \/><\/figure><div class=\"elementor-image-box-content\"><h3 class=\"elementor-image-box-title\">\u0141ukasz Zdanowicz<\/h3><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2680824 elementor-widget elementor-widget-text-editor\" data-id=\"2680824\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Creator of the PhiBoard app. A mathematics enthusiast who firmly believes that building a modern engineering workforce will create prosperity both individually and nationally. Personally, a chess player and a book lover.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-235ce40 elementor-shape-rounded elementor-grid-0 e-grid-align-center elementor-widget elementor-widget-social-icons\" data-id=\"235ce40\" data-element_type=\"widget\" data-e-type=\"widget\" data-no-translation=\"\" data-widget_type=\"social-icons.default\">\n\t\t\t\t\t<style>.elementor-element-235ce40{display:none !important}<\/style>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-850923a elementor-shape-rounded elementor-grid-0 e-grid-align-center elementor-widget elementor-widget-social-icons\" data-id=\"850923a\" data-element_type=\"widget\" data-e-type=\"widget\" data-no-translation=\"\" data-widget_type=\"social-icons.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-social-icons-wrapper elementor-grid\">\n\t\t\t\t\t\t\t<span class=\"elementor-grid-item\">\n\t\t\t\t\t<a class=\"elementor-icon elementor-social-icon elementor-social-icon-tiktok elementor-repeater-item-e92bb2d\" href=\"https:\/\/www.tiktok.com\/@phiboard5\" target=\"_blank\">\n\t\t\t\t\t\t<span class=\"elementor-screen-only\">Tiktok<\/span>\n\t\t\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fab-tiktok\" viewbox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M448,209.91a210.06,210.06,0,0,1-122.77-39.25V349.38A162.55,162.55,0,1,1,185,188.31V278.2a74.62,74.62,0,1,0,52.23,71.18V0l88,0a121.18,121.18,0,0,0,1.86,22.17h0A122.18,122.18,0,0,0,381,102.39a121.43,121.43,0,0,0,67,20.14Z\"><\/path><\/svg>\t\t\t\t\t<\/a>\n\t\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-5fbd114 e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"5fbd114\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-952adb4 e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"952adb4\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d447cbb elementor-widget elementor-widget-text-editor\" data-id=\"d447cbb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>OTHER POSTS<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8281c57 elementor-widget elementor-widget-shortcode\" data-id=\"8281c57\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-shortcode\"><ul class=\"lpt-latest-posts\">        <li>\n            <a href=\"https:\/\/blog.phiboard.com\/en\/wykres-funkcji-liniowej-1\/\">\n\t\t\t\tWykres funkcji liniowej (1)\t\t\t<\/a>\n        <\/li>\n                <li>\n            <a href=\"https:\/\/blog.phiboard.com\/en\/liczby-naturalne-czesc-1\/\">\n\t\t\t\tNatural numbers \u2013 Part 1\t\t\t<\/a>\n        <\/li>\n        <\/ul>\n<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Hi.<\/p>\n<p>I believe that the best way to learn mathematics is by solving problems. Calculating, calculating, and calculating again\u2014starting with the simplest exercises, learning the basic patterns, and gradually progressing to more difficult ones.<\/p>","protected":false},"author":1,"featured_media":1663,"comment_status":"closed","ping_status":"open","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","footnotes":""},"categories":[22,3],"tags":[],"class_list":["post-1600","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-liczby-rzeczywiste","category-matematyka-zadania"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Liczby naturalne - cz\u0119\u015b\u0107 1 - Phiboard<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blog.phiboard.com\/en\/liczby-naturalne-czesc-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Liczby naturalne - cz\u0119\u015b\u0107 1 - Phiboard\" \/>\n<meta property=\"og:description\" content=\"Cze\u015b\u0107. My\u015bl\u0119, \u017ce najlepszym sposobem nauki matematyki jest rozwi\u0105zywanie zada\u0144. 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