What are prime factorization and factor trees?

Answer 1

Factor trees may have been used when you were in elementary school--when you take a number and see what numbers "go into" it by making branches. Prime factorization is simply just a more sophisticated (and kind of easier) way of seeing what PRIME numbers go into a number. To do that, you must divide only use prime divisors. You keep dividing until the last number is 1. Then, using the divisors you've used, you create a multiplication problem, usually with exponents. For example, you have to do the prime factorization of 20. You choose to divide by the Prime number 2, which is 10. You divide 10 by 2 which equals 5, and then you divide by 5 equaling one. Therefore, the prime factorization of 20 is 2 squared times 5.

Answer 2

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: 210

210 Divide by two.

105,2 Divide by three.

35,3,2 Divide by five.

7,5,3,2 Stop. All the factors are prime.

2 x 3 x 5 x 7 = 210

That's the prime factorization of 210.

Answer 3

123

3,41

3 x 41 = 123