Question

Find the GCF. (questions shown in photo)

Answer 1

Given:

(a) $12a^2b^2c, 15a^3b^3c$

(b) $2^3\cdot 3^2\cdot 7\cdot 11\text{ and }2^2\cdot 3^3\cdot 5\cdot 7$

To find:

The GCF.

Solution:

(a)

We have,

$12a^2b^2c, 15a^3b^3c$

The factor forms are

$12a^2b^2c=2\cdot 2\cdot 3\cdot a\cdot a\cdot b\cdot b\cdot c$

$15a^3b^3c=3\cdot 5\cdot a\cdot a\cdot a\cdot b\cdot b\cdot b\cdot c$

Now,

$GCF=3\cdot a\cdot a\cdot b\cdot b\cdot c$

$GCF=3a^2b^2c$

Therefore, the GCF is $3a^2b^2c$.

(b)

We have,

$2^3\cdot 3^2\cdot 7\cdot 11\text{ and }2^2\cdot 3^3\cdot 5\cdot 7$

GCF is the product of common prime factors with least power.

$GCF=2^2\cdot 3^2\cdot 7$

Therefore, the GCF is $2^2\cdot 3^2\cdot 7$.