Question

16. If the HCF of 63 and 117 can be written as 63m + 117n, find the value of m+n.​

Answer 1

If the HCF of 63 and 117 can be written as 63m + 117n, then the value of m+n is 1

Solution:

There are two numbers 63 and 117

Now we can write both numbers as  

$63 = 1 \times 3 \times 3 \times 7\\\\117 = 1 \times 3 \times 3 \times 13$

So HCF of the 63 and 117 is $3 \times 3 = 9$

Now we have according to question that  

63m + 117n = 9

On dividing above equation by 9 we get,

7m + 13n = 1

This can be equal to 1 if m =2 and n=-1

Then in this way , we can find out the value of m+n = 2 - 1 = 1

Hence the value of m + n = 1

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Answer 2

m+n = 1 If the HCF of 63 and 117 can be written as 63m + 117n,

Step-by-step explanation:

117 = 63 × 1. + 54

63 = 54×1 + 9

54 = 9 × 6

HCF = 9

9 = 63 - 54×1

9 = 63 - (117 - 63 × 1) × 1

9 = 63 - 117 + 63

9 = 2 × 63 - 117

9 = 63×2 - 117×1

9 = 63 ×2 + 117(-1)

comparing with

9 = 63m + 117n

m = 2

n = -1

m + n = 2 -1 = 1

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