Class 10 Exam > Class 10 Questions > If A = 2n + 13, B = n + 7, where n is a natur...
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If A = 2n + 13, B = n + 7, where n is a natural number, then HCF of A and B is:
- a)2
- b)1
- c)3
- d)4
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If A = 2n + 13, B = n + 7, where n is a natural number, then HCF of A ...
Taking different values of n we find that A and B are coprime
e.g. put n=1
we get A= 2(1)+13=15
B=1+7=8
∴ HCF = 1
∴ HCF = 1
put n=2
we get A= 2(2)+13=17
B=2+7=9
∴ HCF = 1
∴ HCF = 1
Most Upvoted Answer
If A = 2n + 13, B = n + 7, where n is a natural number, then HCF of A ...
Here is the solution to your question:
A = 2(n + 7) - 1
A = 2B - 1
On dividing throughout with B,
A/B = 2 - (1/B)
B is always an integer => 1/B can never be an integer => A/B also can't be an integer
Since A/B is not an integer we can conclude that A and B cannot have any integer in common.
Therefore, HCF of A and B is 1.
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Community Answer
If A = 2n + 13, B = n + 7, where n is a natural number, then HCF of A ...
The HCF is 1 because there is nothing common in both the equation , except 1
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