Question

What is the prime factorization of 126?


A.


2^2 • 3 • 7


B.


2 • 3 • 7


C.


2 • 3^2 • 7


D.


2 • 3^2 • 72

Answer 1

This is similar to the last multiple choice "what is the prime factorization of" problem. Eliminate the choices that have non prime numbers (like 72).

Then you can just see which one works!

Answer 2

im not really sure about this one i have no idea

Answer 3

I divide by 2 whenever the number is even. So
\(126\div2=63\). So \(126 = 2\times63\)
63 is \(7\times9\), I remember. So \(126 =2\times7\times9\)
7 is okay, it's a prime.
9 is not prime, so we check it out. \(9=3\times3\). So \(126=2\times7\times3\times3\)

\(126=2\times7\times3\times3\) is the prime factorization.

Answer 4

oh so its C

Answer 5

thanks!

Answer 6

You're welcome!

If you want to just go through any number's prime factorization,
divide by 2 when you can
if you can't, divide by 3
if you can't, divide by 5
if you can't, divide by 7
if you can't, divide by 11
and if you can't divide by other primes.

Or, if you see a number like \(120\), go straight for the common sense \(12\times 10\) so you can get right to the lower numbers! But going through the primes is good, too.
\(120=2\times 60\) Side note: 60 is easy, too...
\(120=2\times2\times30\)
\(120=2\times2\times2\times15\)
2 doesn't work.
\(120=2\times2\times2\times3\times5\)
All primes.

Answer 7

Going the other route,
\(120\\=12\times10\\=3\times4\ \times\ 2\times5\\=3\times2\times2\ \times\ 2\times5\)
Same thing, of course.. Same number! :)

Answer 8

I have to go. Take care! Good luck with whatever else you have to do!