Question

Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.

Answer 1

SOLUTION:

To find the greatest number which when divides 285 and 1249 leaving the remainders 9 and 7 respectively.

First ,we subtract the remainder from the given numbers and then calculate the HCF of new numbers.

Given numbers are 285 and 1249 and  remainders are 9 and 7.

Then ,new numbers after subtracting remainders are :

285 - 9 = 276 and 1249 -7 = 1242

Now, we have to find the H.C.F. of 276 and 1242.

By applying Euclid’s division lemma,a = bq+r

Let a = 1242 and b = 276

1242 = 276 x 4 + 138

276 = 138 x 2 + 0.

Here remainder is zero , and the last divisor is 138.

So H.C.F is 138

Hence, the required greatest number is 138

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Answer 2

285-9 =276

1249-7= 1242

By applying euclids division lemma,

1242 = 276*4+138

276 = 138*2+0

Therefore HCF= 138

hence number  required is 138