Question

The sum of two numbers is 1215 and their HCF is 81, then the possible pairs of such numbers are ______.

पर्याय

• 2

• 3

• 4

• 5

Answer 1

The sum of two numbers is 1215 and their HCF is 81, then the possible pairs of such numbers are 4.

Explanation:

The HCF of both numbers is 81.

It means 81 is a factor of both numbers.

Thus, let us assume the numbers are 81x and 81y.

Where x and y are coprime numbers.

Now, given that

Sum of numbers = 1215

81x + 81y = 1215

81(x +y) = 1215

(x + y) = `1215/81`

x + y = 15

Here, x and y are coprime numbers.

So, possible values of x and y can be (1, 14), (2, 13), (4, 11) and (7, 8).

Thus, there are 4 such pairs.