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

Given:

The numbers 525 and 3000 are both divisible only by 3, 5, 15, 25 and 75.

To do:

We have to find HCF (525, 3000)

Solution:

According to Euclid\'s lemma,

Dividend $=$ Divisor $\times$ Quotient $+$ Remainder

This implies,

$3000=525 \times 5+375$

$525=375 \times 1+150$

$375 =150 \times 2+75$

$150=75 \times 2+0$

The numbers 3, 5, 15, 25 and 75 divide the numbers 525 and 3000.

This implies, these terms are common in both 525 and 3000.

Therefore, the highest common factor of 525 and 3000 is 75.

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