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Find the greatest number that will divide 445,

Question:

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

Solution:

Find the greatest number that divides 445, 572 and 699 and leaves remainders of 4, 5 and 6 respectively.

The required number when divides 445,572 and 699 leaves remainders 4,5 and 6 this means $445-4=441,572-5=567$ and $699-6=693$ are completely divisible by the number.

Therefore, the required number = H.C.F. of 441, 567 and 693.

First consider 441 and 567.

By applying Euclid’s division lemma

$567=441 \times 1+126$

$441=126 \times 3+63$

$126=63 \times 2+0$

Therefore, H.C.F. of 441 and 567 = 63

Now, consider 63 and 693

 

By applying Euclid’s division lemma

$693=63 \times 11+0$

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

Hence, the required number is 63

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