MATH SOLVE

5 months ago

Q:
# Which expression shows the prime factorization of 120?A. 2(to the third power) x 3 x 5 B. 2 x 3 x 5C. 10(to the second power)D. 2 x 5 x 12

Accepted Solution

A:

To find the prime factors of a number, start by listing the first several prime numbers: 2, 3, 5, 7, 11, 13, 17, 19

Now divide your number by the smallest prime it divides evenly. Keep dividing by that prime, When you can't divide by that prime anymore, move on to the next one. Keep going until you get 1. All the primes you divided by are the prime factorization of the number.

120 is divisible by 2, so divide 120 by 2.

Then divide 60 by 2. Then divide 30 by 2.

15 is not divisible by 2, so try dividing by 3.

You get 5. 5 is not divisible by 3, so try dividing by 5.

5/5 = 1, so you're done.

See the divisions below. The numbers you divided by are bold. Those are the prime factors.

120/2 = 60

60/2 = 30

30/2 = 15

15/3 = 5

5/5 = 1

120 = 2^3 * 3 * 5

Now divide your number by the smallest prime it divides evenly. Keep dividing by that prime, When you can't divide by that prime anymore, move on to the next one. Keep going until you get 1. All the primes you divided by are the prime factorization of the number.

120 is divisible by 2, so divide 120 by 2.

Then divide 60 by 2. Then divide 30 by 2.

15 is not divisible by 2, so try dividing by 3.

You get 5. 5 is not divisible by 3, so try dividing by 5.

5/5 = 1, so you're done.

See the divisions below. The numbers you divided by are bold. Those are the prime factors.

120/2 = 60

60/2 = 30

30/2 = 15

15/3 = 5

5/5 = 1

120 = 2^3 * 3 * 5