Question

Question 8
Use Euclid’s division algorithm to find the HCF of 441, 567 and 693.

Answer 1

Let a = 693, b = 567 and c = 441
By Euclid's division algorithm,
a = bq + r $[\because dividend=divisor\times quotient+remainder]$
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,
$441=63\times 7+0$

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

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