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

(Q 21 B – 30/4/2 – CBSE 2026 Question Paper)

Ans:

Step 1: By prime factorisation:

210 = 2 x 3 x 5 x 7

55 = 5 x 11

∴ HCF of 210 and 55 = 5

Step 2: By given condition, HCF is expressed as 210 x 5 + 55 m

∴ 210 x 5 + 55 m = 5

∴ 1050 + 55 m = 5

∴ 55 m = 5 – 1050 = – 1045

∴ 11 m = – 209

∴ m = = – 19

Therefore the value of m is – 19.

Check: Value of 210 x 5 + 55 m = 210 x 5 + 55 x (- 19) = 1050 – 1045 = 5
Since HCF value of 210 & 55 is 5. It meets the given condition. Hence our solution is correct.

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