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.
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a
|
b
|
|
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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
|