Question

Find the greatest number that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively.

Answer 1

SOLUTION :

To find the greatest number which when divides 445, 572 and 699  leaving the remainders  4, 5 and 6 respectively. First ,we subtract the remainder from the given numbers and then calculate the HCF of new numbers.

Given numbers are  445, 572 and 699 and  remainders are  4, 5 and 6

Then ,new numbers after subtracting remainders are :

445 – 4 = 441, 572 – 5 = 567 and 699 – 6 = 693  

Now, we have to find the H.C.F. of 441, 567 and 693.

First we find the HCF of  441 and 567.

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

Let a = 567 and b = 441

567 = 441 x 1 + 126

441 = 126 x 3 + 63

126 = 63 x 2 + 0.

Here remainder is zero , and the last divisor is 63.

So H.C.F of  441 and 567 is 63

Now,we find the HCF of 63 and 693

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

Let a = 693  and b = 63

693 = 63 x 11 + 0.

Here remainder is zero , and the last divisor is 63

So H.C.F. of 63 and 693 is  63.

Therefore,H.C.F. of 441, 567 and 693 is 63.

Hence, the required greatest number is 63.

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