Question

Q47. Find the greatest number which divides 285 and 1249, leaving remainders 9
and 7 respectively.
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Answer 1

Step-by-step explanation:

THE GREATEST NUMBER WHICH DIVIDES 285 AND 1249 LEAVING REMINDERS 9 AND 7 IS 138.

New numbers after subtracting remainders are :

285 – 9 = 276

1249 – 7 = 1242.

The required number is HCF of 276 and 1242.

Prime factorization of 276 = 2×2×3×23 = 2² × 3¹ × 23¹

Prime factorization of 1242 = 2×3×3×3×23 = 2¹ × 3³ × 23¹

HCF of 276 and 1242 = 2¹ ×3¹×23¹

= 6 × 23 = 138