Question

Use Euclid’s division algorithm to find the HCF of 441, 567 and 693.

• A. 63
• B. 58
• C. 49
• D. 82

Answer 1

The correct option is A 63

Let a = 693, b = 567 and c = 441
By Euclid's division algorithm,
$a=bq+r....[\because \text{dividend = divisor}\times \text{quotient + remainder}]$
First, we take, a = 693 and b = 567. Find their HCF.
$693=567\times 1+126$
$567=126\times 4+63$
$126=63\times 2+0$
HCF (693, 567) = 63

Now to find the HCF of 441, 567 and 693, we find the HCF of 441 and the HCF of 563 and 697, which is 63, using Euclid's division aigorithm,
Now HCF of 441 and 63
$441=63\times 7+0$

Since the remainder is 0, the HCF of 441 and 63 is 63.

Thus, HCF (693, 567, 441) = 63