Question

find the largest number that will divide 445 572 and 699 leaving remainders 4 5 and 6 respectively​

Answer 1

Answer:

Solution-> 445 - 4 = 441

572 - 5 = 567

699 - 6 = 693

Now find the greatest common factor of those 3 numbers:

441 = 3 x 3 x 7 x 7

572 = 3 x 3 x 3 x 3 x 7

693 = 3 x 3 x 7 x 11

The common factors are 3 x 3 x 7 = 63

HCF Of (441,567,693) = 63

445 / 63 = 7 remainder 4

572 / 63 = 9 remainder 5

699 / 63 = 11 remainder 6

Answer:

63 is the largest divisor that will give the desired remainders

Answer 2

Answer:

The required number when divides 445, 572 and 699 leaves remainders 4, 5 and 6

This means 445 – 4 = 441, 572 – 5 = 561 and 699 – 6 = 693 are completely divisible by the number

∴ The required number = HCF of 441, 567 and 693

First consider 441 and 567

By applying Euclid’s division lemma

567 = 441 × 1 + 126

441 = 126 × 3 + 63

126 = 63 × 2 + 0

∴ HCF of 441 and 567 = 63

Now consider 63 and 693

By applying Euclid’s division lemma

693 = 63 × 11 + 0

∴ HCF of 441, 567 and 693 = 63

Hence required number is 63.