The sum of two numbers is 36 and their HCF is 4. Find the possible num

1.	The sum of two numbers is 36 and their HCF is 4. Find the possible number of pairs.1. 32. 43. 54. 6
Answer» Correct Answer - Option 1 : 3 Given: Sum of numbers = 36 HCF = 4 Concept used: The H.C.F. of two or more than two numbers is the greatest number that divides each of them exactly. Calculation: Let, the numbers are 4x and 4y ⇒ 4x + 4y = 36 ⇒ 4(x + y) = 36 ⇒ x + y = 9 ⇒ (1, 8) ⇒ (2, 7) ⇒ (4, 5) We can see the 3 possible pairs. ∴ The possible number of pairs is 3. To find the pairs we only can take those pair which are prime to each other. We can't take those pair which are not prime to each other. For example: In this problem, 9 can be represent as 6 + 3 = 9 But, 6 & 3 are not prime to each other. So, it can't be a possible pair.

The sum of two numbers is 36 and their HCF is 4. Find the possible number of pairs.1. 32. 43. 54. 6

Answer» Correct Answer - Option 1 : 3

Given:

Sum of numbers = 36

HCF = 4

Concept used:

The H.C.F. of two or more than two numbers is the greatest number that divides each of them exactly.

Calculation:

Let, the numbers are 4x and 4y

⇒ 4x + 4y = 36

⇒ 4(x + y) = 36

⇒ x + y = 9

⇒ (1, 8)

⇒ (2, 7)

⇒ (4, 5)

We can see the 3 possible pairs.

∴ The possible number of pairs is 3.

To find the pairs we only can take those pair which are prime to each other. We can't take those pair which are not prime to each other.

For example: In this problem, 9 can be represent as 6 + 3 = 9

But, 6 & 3 are not prime to each other. So, it can't be a possible pair.

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