The sum of two numbers is 156 and their H.C.F is 12. Find the number o

1.	The sum of two numbers is 156 and their H.C.F is 12. Find the number of such pairs1. 12. 23. 34. 6
Answer» Correct Answer - Option 4 : 6 Given: Sum of the numbers = 156 H.C.F of numbers = 12 Concept used: If H.C.F of two numbers is H, then number are Hx and Hy. Where x and y are relatively prime number or coprimes. Calculation: Let numbers are 12x and 12y, where x and y are coprimes Now, 12x + 12y = 156 ⇒ 12 (x + y) = 156 ⇒ x + y = 156/12 = 13 ∴ possible values if x and y are (x = 1, y = 12), (x = 2, y = 11) (x = 3, y = 10), (x = 4, y = 9) (x = 5, y = 8), (x = 6, y = 7) Therefore, possible numbers of pairs = 6

The sum of two numbers is 156 and their H.C.F is 12. Find the number of such pairs1. 12. 23. 34. 6

Answer» Correct Answer - Option 4 : 6

Given:

Sum of the numbers = 156

H.C.F of numbers = 12

Concept used:

If H.C.F of two numbers is H, then number are Hx and Hy. Where x and y are relatively prime number or coprimes.

Calculation:

Let numbers are 12x and 12y, where x and y are coprimes

Now, 12x + 12y = 156

⇒ 12 (x + y) = 156

⇒ x + y = 156/12 = 13

∴ possible values if x and y are

(x = 1, y = 12), (x = 2, y = 11)

(x = 3, y = 10), (x = 4, y = 9)

(x = 5, y = 8), (x = 6, y = 7)

Therefore, possible numbers of pairs = 6

Discussion

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