Question

Using euclids division lemma, find the HCF of
(a) 10224 and 9648
(b) 441,567 and 693

Answer 1

$\bold{(a) 10224\:and\:9648}$

Answer ➡

Euclids division lemma => a = bq+r

Substitute the values.

[a = 10224 and b = 9648]

➡ 10224 = 9648 ×1 + 576.

[a = 9648 and b = 576]

➡ 9648 = 576 × 16 + 432

[a = 576 and b = 432]

➡ 576 = 432 × 1 + 144

[a = 432 and b = 144]

➡ 432 = 144 × 3 + 0.

As remainder is 0, HCF = 144.

$\bold{(b) 441\:,\:567\:and\:693}$

Answer ➡

Euclids division lemma => a = bq+r

Substitute the values.

[a = 567, b = 441]

➡ 567 = 441 × 1 + 126

[a = 441, b = 126]

➡ 441 = 126 × 3 + 63

[a = 126, b = 63]

➡ 126 = 63 × 2 + 0

Therefore HCF of (567,441) = 63

Now find the HCF of 693 and 63

[a = 693 , b = 63]

➡ 693 = 63 × 11 + 0

Therefore HCF (693,63) = 63

From the above we can say that HCF of (441,567,693) = 63