If the HCF of 65 and 117 is in the form 65 m – 117, then the value of m is.

Question

Question

This question was previously asked in

Bihar STET TGT (Maths) Official Paper-I (Held On: 04 Sept, 2023 Shift 1)

Answer 1

Explanation -

Applying the Euclidean algorithm:

\( 117 = 65 \times 1 + 52 \\ 65 = 52 \times 1 + 13 \\ 52 = 13 \times 4 + 0 \)

Therefore, the HCF of 65 and 117 is 13.

Now, we're given that the HCF of 65 and 117 is in the form 65m - 117.

We've already found that the HCF is 13.

So, 65m - 117 = 13.
65m = 13 + 117
65m = 130
m = 2

Therefore, the value of m that satisfies 65m - 117 = 13 is m = 2.