Question

Find the greatest number that will divide 445 572 and 699

Answer 1

Answer: 3

Step-by-step explanation:

The factors of 699 are: 1, 3, 233, 699

The factors of 445572 are: 1, 2, 3, 4, 6, 9, 12, 18, 36, 12377, 24754, 37131, 49508, 74262, 111393, 148524, 222786, 445572

Then the greatest common factor is 3

Answer 2

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.

Hope this helps