Incredible Numbers! vs Prime Factorization Deluxe

Selected by Apple as Best of 2014, and winner of the 2015 Digital Book Award for Best Nonfiction App. Bestselling author Professor Ian Stewart is your guide through Incredible Numbers. Numbers define the patterns of sunflowers; they bring pleasure through music; and they help us answer existential questions like; ‘How many ways are there to lace my shoes?’ Interactive examples – from simple equations to a working Enigma machine – put the beautiful concepts behind mathematics at your fingertips. “A measure of Ian Stewart’s success is that he’s able to give a clear path through some very hairy mathematics.” – Times Higher Education Supplement There’s so much more than a few screenshots can show: – 23 articles crafted by Prof. Ian Stewart, embedded with 71 groundbreaking interactive demonstrations. – 23 bespoke interactive sections that let you immerse yourself in the beautiful patterns and concepts behind each topic. – 15 of Ian Stewart’s famous mathematical puzzles. Topics include: • Infinity – Explore infinity and understand what it really means to say something is infinite. • Pi – Unwrap the mysteries of pi to see why this strange number is so important and why it’s not just about circles. • Music – Music and math share the beauty of finding patterns in complexity. Detailed interactives show you how they relate in real, meaningful and fun ways. • Codes – See how the power of numbers can unlock complexity in codes. • Nature – See how numbers work in nature by looking at the Fibonacci sequence and how it appears in the real world in beautiful and surprising ways. • Primes – Discover the mysterious patterns in prime numbers, and why they are so important. • Polygons – Get to grips with shapes and polygons. Classical geometry is just another way to think about numbers! • Factorials – How many ways can you lace your shoes? Did you know that if you have 4 eyelets, there are 24 possible lacing styles? With 12 eyelets there are 479,001,600 possibilities. See why this is so in Factorials! Incredible Numbers aspires to convince you that maths is beautiful. Mathematicians know this already. The great solutions and proofs shine to them, but their underlying beauty has been hidden behind abstract algebra and complex equations. Until now. If you enjoy this app, don’t forget to rate it in the App Store.

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.