Question

lf HCF of 171 & 95 is A and is
expressible in the form of 95 m+171 n
then the value of A+m+n are
respectively​

Answer 1

Given:

• HCF of 171 and 95 is A
• A can be expressed as 95m + 171n

To find: the value of A + m + n

Solution:

• 171 = 1 × 3 × 3 × 19
• 95 = 1 × 5 × 19
• So HCF of 171 and 95 is (1 × 19) = 19.
• Thus, A = 19.

We have: 171 = 95 × 1 + 76

95 = 76 × 1 + 19

76 = 19 × 4

Now, 95 = 76 × 1 + 19

or, 19 = 95 - 76 × 1

= 95 - (171 - 95 × 1) × 1

= 95 - 171 × 1 + 95 × 1

= 95 × 2 - 171 × 1 ... ...(1)

We have: 19 = 95m + 171 and comparing with (i), we get

• m = 2 and n = - 1

Now, A + m + n = 19 + 2 - 1 = 20

Answer: A + m + n = 20