find the greatest number which divides 285 and 1249 leaving remainder 9 and 7 respectively .
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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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