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Q.

If HCF of 65 and 117 is expressible in the form ofQuestion Image, then determine the value of n.


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a

2

b

1

c

4

d

5 

answer is A.

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Detailed Solution

Concept- In this problem, the given numbers will first be written as the sum of their prime factors. The Highest Common Factor among the given numbers will then be determined. Calculate the HCF of first and second given numbers using the given expression. And then find the values of n by further solving the equation.
In this question, the given numbers are 65 and 117.
First, we will determine the HCF of 65 and 117.
After factoring 65 and 117, we will represent the two numbers as the sum of their prime factors.

5

65

13

13

 

1

Question Image

3

117

3

39

13

13

 

1

⇒117=3×3×13
Now the HCF of 65 and 117 is 13.
As per the given question,
Question ImageHence, the correct answer is option 1.
 
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If HCF of 65 and 117 is expressible in the form of, then determine the value of n.