Prime Factorization Deluxe vs Numbers & Place Value

Use Prime Factorization Deluxe to explore and learn how to find the prime factorization of a composite number. Use the slider to select a number up to 100 for factorization. If a composite number is selected the app prompts the user to select a factor using the slider. If a prime is selected it is indicated using a red marker. Tap the question mark for a random number up to 100 to be automatically selected. Choose factors for the given number to build a factor tree. Continue until the prime factorization has been found. Learn how to find the Greatest Common Factor (GCF) and Least Common Multiple (LCM). For GCF, use the number line slider to select two numbers. The factors of the two numbers are show in a table and the greatest common factor is highlighted. For LCM, choose two numbers. The multiples of the number are shown in a table. The least common multiple is highlighted in the table. The first step in the process of prime factorization is to select a factor for the given number. If a factor is selected a branch on the tree is filled in. This process continues until all the composite numbers in the tree have been factored leaving only primes. Composite numbers are shown in blue and primes are highlighted in red. By examing the prime factorizations of two numbers students will notice that the Greatest Common Factor of two numbers is precisely the product of the primes that are common to both. Therefore it follows that the common multiples of any two numbers must contain each of the primes exactly once and that the least common multiple is the smallest number that occurs in both sets.

Explore large and small numbers and discover how place value works – interactively. This is not a drill app but an open environment for exploring and experimenting. Understanding place value is one of the most important foundations in mathematics: it underpins mental and written calculation strategies, decimals and much more. HOW IT WORKS Drag the digits up and down with your finger. Go beyond 9 and watch ten items bundle into one item of the next place. Go below 0 and see how the next place is "unbundled". Swipe or tap the quantity below a digit to change it. At the bottom of the screen, choose how the quantity is shown: place value counters, base-ten (Dienes) blocks, euro money, dot fields, 3D base-ten material and more. TOOLS ON THE RIGHT - Speaker: listen to the number being read aloud. - Speech bubble with check mark: read the number aloud yourself and check whether you read it correctly. - Expand: shows, for example, 142 as 100 + 40 + 2. - Dice: roll a random new number. - Speech bubble with dots: say a number and watch it appear. - Question mark: some places are covered, the number is read aloud and you fill in the missing digits. MORE OPTIONS - Use the grey arrows to add or remove places – explore numbers up to 100 trillion. - Move the decimal point to work with decimals down to millionths. - Tap a place label (O, T, H …) to change its color. - Swipe across a digit to cover it; tap the cover to enter your answer and get feedback. - Number words above the digits in matching place colors – optionally as "Say Ten" number words (e.g. 284 = "two hundred eight ten four"). - Many settings in the app: thousands separator, place labels, speech rate, show or hide tools and representations, protect settings. - Share a setup or task with your class via QR code. - English (UK/US) and German. - Also available in the browser: zahlen.urff.app IDEAS FOR THE CLASSROOM - Number dictation: show 3,469. - Keep adding one to the ones. What happens when you go past 9? - Show 340. What happens when you take one away from the ones? What about 300? - Show 5,216 and expand it: which numbers make it up (5,000 + 200 + 10 + 6)? What about 5,316? - Listen to a number, then change one place. Can you read the new number correctly? - Tap the question mark and solve some tasks – the app counts them for you. - Why does the leading zero in 0453 disappear? Why does the zero stay in 204 or 240?