Question

Write 3600 as a product of prime factors. Give your answer in index form

Answer 1

Answer:

2⁴×5²×3² is the correct answer

Answer 2

Step-by-step explanation:

The process of finding the Prime Factors of 3600 is called Prime Factorization of 3600. To get the Prime Factors of 3600, you divide 3600 by the smallest prime number possible. Then you take the result from that and divide that by the smallest prime number. Repeat this process until you end up with 1.

This Prime Factorization process creates what we call the Prime Factor Tree of 3600. All the prime numbers that are used to divide in the Prime Factor Tree are the Prime Factors of 3600. Here is the math to illustrate:

3600 ÷ 2 = 1800

1800 ÷ 2 = 900

900 ÷ 2 = 450

450 ÷ 2 = 225

225 ÷ 3 = 75

75 ÷ 3 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

Again, all the prime numbers you used to divide above are the Prime Factors of 3600. Thus, the Prime Factors of 3600 are:

2, 2, 2, 2, 3, 3, 5, 5.