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`.