# How Many Pairs of Such Numbers are Possible?

The H.C.F of two numbers is 67 and their sum is 670. How many pairs of such numbers are possible?

- 5
- 2
- 1
- 3

**Answer: (1) 5**

**Explanation:-
**The H C F of two numbers = 67

Then, the numbers will be 67 X and 67 Y

Where, X and Y are the prime numbers.

Their sum is 670,

Then, 67X + 67 Y = 670

X + Y = 670/67

X + Y = 10

Then, the pairs are which sum is 10 = (1, 9), (2, 8), (3, 7), (4, 6), (5, 5)

There are only 5 pairs which sum is 10.

Then, edupil the pairs are which sum is 670 = (67 x 1, 67 x 9), (67 x 2, 67 x 8), (67 x 3, 67 x 7), (67 x 4, 67 x 6), (67 x 5, 67 x 5)

= (67, 603), (134, 536), (201, 469), (268, 402), (335, 335).

Hence, the answer is (1) 5.