The product of two numbers is 2028 and their HCF is 13. What are the number of such pairs?
Pick one.
A) 1  B) 2  C) 5  D) 23  E) 25
Let the numbers be 13x and 13y ( HCF of the numbers = 13)   13x × 13y = 2028   xy = 12   co-primes with product 12 are (1, 12) and (3, 4) ( we need to take only   co-primes with product 12. If we take two numbers with product 12, but not co-prime,   the HCF will not remain as 13)   Hence the numbers with HCF 13 and product 2028   = (13 × 1, 13 × 12) and (13 × 3, 13 × 4)   = (13, 156) and (39, 52)   So, there are 2 pairs of numbers with HCF 13 and product 2028   Answer is 2
<result>B</result>
The product of two numbers is 2028 and their HCF is 13. What are the number of such pairs?