Correct Answer - Option 2 : 2
Given:
L.C.M of two numbers = 640
H.C.F of two numbers = 16
Concept used:
If H.C.F of two natural numbers is H, then numbers should be Hx and Hy respectively, where x and y should be relatively prime number.
Formula used:
The Product of H.C.F and L.C.M of any two numbers is equal to the product of that numbers.
Calculation:
Let, numbers be 16x and 16y respectively.
Using formula,
⇒ 16x × 16y = 16 × 640
⇒ x × y = 640/16 = 40
⇒ x × y = 40
Possibilities of x, y = (1, 40), (2, 20), (4, 10), (5, 8)
Here, only (1, 40), (5, 8) are such pairs of relatively prime numbers.
∴ Only two pairs are possible.
Prime Number:
1. A prime number is a number that has only two factors, that is, 1 and the number itself.
2. A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.
