High School

If the H.C.F of 210 and 55 is expressible in the form of \( 210 \times 5 + 55y \), find \( y \).

Answer :

Answer:

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

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