HCF of two number is 4 and the sum of those two numbers is 36. Find how many such pair of number is possible.

Question

Question

Answer 1

Given:

HCF of two number is 4 and the sum of those two numbers is 36.

Concept Used:

Concept of HCF

HCF is the least common factor among two or more numbers.

Calculation:

HCF of two number is 4

Let, those numbers be 4x and 4y where x and y are prime to each other

Accordingly,

4x + 4y = 36

⇒ 4(x + y) = 36

⇒ (x + y) = 9

Now,

9 = 8 + 1

9 = 7 + 2

9 = 6 + 3

9 = 5 + 4

In all these cases only (8,1); (7,2); and (5,4) are prime to each other. So, such three pair is possible

∴ Such three pair of number is possible.

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