Can someone list the amount of numbers that have a GCF of 7 and a product of 490?

The amount of numbers that have a G C F of 7 and a product of 490 is 2.

Step-by-step explanation:

On Prime Factorization 490 = 2 x 5 x 7 x 7

G CF = Greatest Common Factor

So, here the possible number who have products as 490 and G C F as 7 is

(a) 2 x 7 = 14 and 5 x 7 = 35

As, 14 and 35 on multiplication, gives 490 as a product.

And, G C F of 14 and 3 5 is also 7.

(b) 7 and 5 x 7 x 2 = 70

As, 7 and 70 on multiplication, gives 490 as a product.

And, G C F of 7 and 70 is also 7.

⇒ (14, 35) and (7,70) are the only such pairs.

Hence, the amount of numbers that have a G C F of 7 and a product of 490 is 2.