Question

find the greatest number which divides 285and1249 leaving remainder 9and7respectively​

Answer 1

To find the largest number which when divided 285 and 1249 leaving the remainder 9 and 7 respectively. First, we subtract the remainder from the given numbers and then calculate the HCF of new numbers.

Answer:

Given numbers are 285 and 1249 and remainders are 9 and 7 respectively. Then new numbers after subtracting remainders are :

285 – 9 = 276

1249 – 7 = 1242.

The required number is HCF of 276 and 1242.

HCF by prime factorization method :

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

[HCF of two or more numbers =  product of the smallest power of each common prime factor involved in the numbers.]

HCF of 276 and 1242 is 138.

Hence, the required greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively is 138.

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