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