GCF and LCM · part 2 of 7
Breaking a Number into Prime Factors
Factor trees. Split, keep splitting, circle it when it is prime.
Step 1: break both numbers into primes
A prime (a whole number bigger than 1 whose only factors are 1 and itself) cannot be broken down any further. 2, 3, 5, 7, 11, 13, 17 and on forever. That list never stops, so do not read the first few as the whole list: 29 is prime, 101 is prime, and they keep coming. Every other whole number is built by multiplying primes together, and there is only one way to build it.
To break a number down, draw a factor tree. Split the number into any two factors that multiply to it, then keep splitting each one. Circle it when it is prime.
Breaking 24 down
24 = 2 x 2 x 2 x 3
Breaking 36 down
36 = 2 x 2 x 3 x 3
It does not matter which pair you start with. Split 24 as 3 times 8 instead and the bottom row comes out the same:
The same 24, started a different way
24 = 2 x 2 x 2 x 3
Those two bottom rows are the raw material. Everything else in this lesson is just looking at them side by side.