If the HCF of two natural numbers whose sum is 216 is 12, how many such pairs exist?
Answer: 3 pairs
Explanation:
Let the two number be 12a and 12b where a and b are relatively prime.
Then 12a + 12b = 216
a + b = 18
Now, this boils down to finding out all possible ways of writing 18 as a sum of two natural numbers coprime to each other.
a

b


17

1

ü

16

2

X

15

3

X

14

4

X

13

5

ü

12

6

X

11

7

ü

10

8

X

9

9

X

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