Split until prime

About this video

Everything around you is made of a few kinds of atoms. Whole numbers have atoms too, when you build them by multiplying: the prime numbers. Every composite number can be broken down into primes multiplied together, and a factor tree is how you find them. This short animation grows one for 60.

60 is composite, so it splits into a factor pair, two factors that multiply to make it: 6 × 10. Each branch is then looked at on its own. 6 is composite, so it splits into 2 × 3. 10 is composite too, so it splits into 2 × 5. Now the ends of the branches are 2, 3, 2 and 5. They are all primes and can't split any more, so they are ringed and the tree is finished. The ringed numbers are the prime factors of 60: 60 = 2 × 2 × 3 × 5.

A factor tree can always be checked by multiplying back: 2 × 2 = 4, 4 × 3 = 12, and 12 × 5 = 60. The rule for growing a tree is simple: split a composite number into a factor pair, and ring a prime and stop. A prime's tree is the shortest of all: 13 can't split, so its tree is just 13, ringed. This video goes with the Factor Trees lesson of Number Theory Level 1 on Knaph.

Transcript

1. 0:00Numbers have atoms too. They're the primes.
2. 0:05Split sixty into a factor pair. Six times ten.
3. 0:10Six is two times three. Ten is two times five. All primes now.
4. 0:16Sixty is two times two times three times five.
5. 0:21Check it by multiplying back. Four, twelve, sixty.
6. 0:26A prime's tree is just itself.
7. 0:30Split, and split again, until only primes are left.