If the H. C. F of 210 and 55 is expressible in the form of 210*5 + 55y, find 'y'?

y = - 19

Step-by-step explanation:

Express 210 and 55 as products of their prime factors, that is

210 = 2 * 3 * 5 * 7

55 = 5 * 11

Identify the prime factors that both numbers have in common and multiply them.

Here only 5 is common, thus

HCF = 5

Thus

5 = 210 * 5 + 55y, that is

5 = 1050 + 55y (subtract 1050 from both sides)

- 1045 = 55y (divide both sides by 55)

y = - 19