Question

Find the greatest number that divides 1085 and 1514, leaving remainders of 5 and 2, respectively​

Answer 1

Answer:

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Find the greatest number that divides 1085 and 1514, leaving remainders of 5 and 2, respectively

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Find that number

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Subtract 5 , 2 from 1085 and 1514 resp.

1085 - 5 = 1080

1514 - 2 = 1512

Find hcf of both

1080 = 2 × 2 × 2 × 3 × 3 × 3 × 5

1512 = 2 × 2 × 2 × 3 × 3 × 3 × 7

Hcf = 2 × 2 × 2 × 3 × 3 × 3

= 216

Hcf of 1080 and 1512 = 216

Therefore, 216 is the greatest number that when divides 1085 leaves remainder 5 and when divides 1514 leaves remainder 2.

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Answer 2

Subtract 5 , 2 from 1085 and 1514 resp.

1085 - 5 = 1080

1514 - 2 = 1512

Find hcf of both

1080 = 2 × 2 × 2 × 3 × 3 × 3 × 5

1512 = 2 × 2 × 2 × 3 × 3 × 3 × 7

Hcf = 2 × 2 × 2 × 3 × 3 × 3

= 216

Hcf of 1080 and 1512 = 216

Therefore, 216 is the greatest number that when divides 1085 leaves remainder 5 and when divides 1514 leaves remainder 2.