Prime factorization is breaking down a number into all of the prime numbers that make it up.
For example, in 128, since it is even, the easiest first step would be diving by two, a Prime number.
64 * 2 = 128. Now divide 64, another even number, by two.
32 * 2 * 2 = 128. Divide 32 by two.
16 * 2 * 2 * 2 = 128. Divide by two again.
8 * 2 * 2 * 2 * 2 = 128. Divide by two again.
4 * 2 * 2 * 2 * 2 * 2 = 128. Divide by two a final time.
2 * 2 * 2 * 2 * 2 * 2 * 2 = 128. This is your prime factorization.
But you write it condensed, so 27 would be the prime factorization for 128.
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128 = 27
2^7
The prime factorization of 128 is: 2 x 2 x 2 x 2 x 2 x 2 x 2 or 27
128 64,2 32,2,2 16,2,2,2 8,2,2,2,2 4,2,2,2,2,2 2,2,2,2,2,2,2
Well, honey, the prime factorization of 128 is 2^7. Yep, that's right, just a whole lotta twos multiplied together to give you that big ol' 128. Math can be a real hoot sometimes, can't it?