Question

The product of two numbers is 5292 and their H.C.F. is 21. The number of such pairs is:

• A. 1
• B. 4
• C. 2
• D. 3

Answer 1

Answer:

C. 2

Let the two numbers be 21a and 21b(since hcf = 21 and gcd =1)

$21a\times21b$ = 5292

441ab = 5292

$ab = \frac{5292}{441}$

ab = 12 and gcd(a,b) = 1

factor pairs of 12:

(1,12),(2,6),(3,4)

valid pairs are (1,12),(3,4)

each gives a pair of numbers (21,252)(63,84)

so total number of such pairs = 2