# Find the number of pairs of two numbers whose HCF is 5 and their sum is 50. kindly help!?

### 5 Answers

- Ian HLv 71 year ago
At first we might think of this list

5, 45

10, 40

15, 35

20, 30

25, 25

But 10 rather than 5 is the HCF with

10, 40 and

20, 30

and 25, 25 obviously has an HCF of 25,

so that just leaves 5, 45 and 15, 35

- AmyLv 71 year ago
Both numbers are multiples of 5, so let's call them 5x and 5y.

The constraint is that x and y are positive integers and are relatively prime to each other.

5x + 5y = 50

x + y = 10

List all pairs (x,y) that sum to 10 and meet the stated constraint.

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- PopeLv 71 year ago
It should take only a moment to check all non-negative integer pairs that are divisible by five and whose sum is 50. Let the first of the pair increase from zero to 25.

0, 50 ... HCF = 50; reject

5, 45 ... HCF = 5

10, 40 ... HCF = 10; reject

15, 35 ... HCF = 5

20, 30 ... HCF = 10; reject

25, 25 ... HCF = 25; reject

I count two qualifiers.