Question

If the HCF of 210 and 55 is expressed as 210 × 5 + 55m, then find the value of m.

Answer 1

Given:

HCF (210, 55) = 210 × 5 + 55m

HCF of 210 and 55

Using Euclid’s algorithm:

210 = 55 × 3 + 45

55 = 45 × 1 + 10

45 = 10 × 4 + 5

10 = 5 × 2 + 0

The remainder has become zero, so the HCF is 5.

Now, substitute this value into the given equation:

5 = 210 × 5 + 55m

5 = 1050 + 55m

55m = 5 – 1050

55m = –1045

`m = (-1045)/55`

`m = (-95)/5`

m = –19

The value of m is –19.