Find the largest two digit number that divides 673

Asked by admin @ 11/08/2021 in Math viewed by 817 People

Find the largest two digit number that divides 673 and 865, leaving remainder 1 in each.

Answered by admin @ 11/08/2021

Solution :-

To find the largest two digit number that divides 673 and 865, leaving remainder 1 in each case, first we have to subtract 1 from both the numbers and then we will compute H.C.F. of both the numbers.

⇒ 673 - 1 = 672
⇒ 865 - 1 = 864

H.C.F. of 672 and 864

___________
2 |672, 864
|___________
2 |336, 432
|___________
2 |168, 216
|___________
2 | 84, 108
|___________
2 | 42, 54
|___________
3 | 21, 27
|___________
| 7, 9

H.C.F. of 672 and 864 = 2*2*2*2*2*3 = 96

So, 96 is the largest two digit number that 673 and 865, leaving remainder 1 in each case.

_____________________________________________________________

Let us check our answer.

865 ÷ 96

Quotient = 9

Remainder = 1

673 ÷ 96

Quotient = 7

Remainder = 1

So, our answer is correct.

Find the largest two digit number that divides 673

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