Question

A number is written with the following factorization 2 x 3 x 5^4 x 8 x 11^2 . Is this factorization a prime factorization? Explain why or why not. If it is not correct, give the correct prime factorization of the number.

Answer 1

@Directrix @Nnesha @WanderingGirl

Answer 2

Do you know what a prime number is?

Answer 3

yes

Answer 4

are there any numbers in your list of factors that are not prime?

Answer 5

(not including exponents of course)

Answer 6

what list of factors

Answer 7

Up there in your question, you have a "list" of factors. I will state them explicitly: 2, 3, 5, 5, 5, 5, 8, 11, 11. Which, if any, are not prime?

Answer 8

8 is not prime

Answer 9

correct. What is the prime factorization of 8? do you know?

Answer 10

2^3

Answer 11

good. Now we can rewrite your list of factors as: 2, 2, 2, 2, 3, 5, 5, 5, 5, 11, 11. Do you understand how i did this?

Answer 12

mmm not really

Answer 13

well, since 8 = 2^3, we can say that 8=2*2*2, so instead of an 8 in your list of prime factors, I instead inserted three twos. Make sense?

Answer 14

oh yes i understand

Answer 15

ok, now all that is left is to multiply and condense the factors. do you know how to do that?

Answer 16

i can multiply the factors but what is condense the factors

Answer 17

condense is to write them in exponent form. DON'T actually multiply them, just write them in exponent form. for example, {2, 2, 2, 2} is just 2^4

Answer 18

yes

Answer 19

can you do that?

Answer 20

yes

Answer 21

ok tell me what you get

Answer 22

2^4 x 3 x 5^4 x 11^2

Answer 23

\[\huge 2^4\times3\times5^4\times11^2\]

Answer 24

This is correct

Answer 25

yes

Answer 26

so it is a prime factorization

Answer 27

Yes this is the prime factorization

Answer 28

thank you

Answer 29

it says explain

Answer 30

can you explain why

Answer 31

No problem. Medal Please! Your explanation is that all of the factors listed are primes raised to exponents, thus the product represents the prime factorization

Answer 32

thank you and here is a medal

Answer 33

great thanks!