What is a prime power factorization?

Answer 1

All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.

Example: 216

216 Divide by two.

108,2 Divide by two.

54,2,2 Divide by two.

27,2,2,2 Divide by three.

9,3,2,2,2 Divide by three.

3,3,3,2,2,2 Stop. All the factors are prime.

2 x 2 x 2 x 3 x 3 x 3 = 216

Repeated factors can be abbreviated by the use of exponents (powers).

23 x 33 = 216

That's the prime power factorization of 216.

Answer 2

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