# Greatest Common Factors

#### kconstien

##### New member
I do not understand GCF, do you need to factor down each number for instance
the GCF for 1200 and 450
Would that be 2 or 150?

and for 11b6, 11b4k2, 19b4
would this be b4?

#### royhaas

##### Full Member
The greatest common factor of 1200 and 450 is 150, since 1200=150*8, 450=150*3, and the greatest common factor of 3 and 8 is 1. You should factor both numbers into a product of prime powers.

#### kconstien

##### New member
Thank you for that. I wasn't sure if you had to factor all the way down.

Could you help me with the other one.
11b*6, 11b*4K*2, 19b*4

I think this would be b*4 since I don't see anything in commone with the whole number.

Thanks.

#### Denis

##### Senior Member
kconstien said:
11b*6, 11b*4K*2, 19b*4
I think this would be b*4 since I don't see anything in commone with the whole number.
What do you mean with b*6; b to the power 6? If so, show this way: b^6.
If you mean b times 6, then 11b*6 = 66b: quite a different animal!

#### kconstien

##### New member
Thank you, I'm a total rookie!

The question is find the GCF of

11b^6, 11b^4k^2, 19b^4

#### stapel

##### Super Moderator
Staff member
Follow the same process explained earlier: Factor each term completely. The greatest common factor will be the product of the factors that each term shares.

Eliz.

#### Denis

##### Senior Member
kconstien said:
The question is find the GCF of
11b^6, 11b^4k^2, 19b^4
Sometimes easier if you pretend you're adding the terms:
11b^6 + 11b^4k^2 + 19b^4
= b^4(? + ? + ?)