Problem solving - numbers


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 co-prime 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