Question

Question 6
The numbers 525 and 3000 are both divisible only by 3, 5, 15, 25 and 75. What is the HCF (525, 3000)? Justify your answer.

Answer 1

Since, the common factors of 525 and 3000 are 3, 5, 15, 25, 75.
So, HCF (525 and 3000) = 75
Finding HCF by Euclid's Lemma, $3000=525\times 5+375$
$[\because \text{Dividend}=\text{Divisor}\times \text{Quotient}+\text{Remainder}]$
$525=375\times 1+150$
$375=150\times 2+75$
$150=75\times 2+0$
$\Rightarrow$ HCF (525 and 3000) = 75

The numbers 3, 5, 15, 25 and 75 divides the numbers 525 and 3000. It means these terms are common in both 525 and 3000.
So, the highest common factor among these is 75.