Question

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

Answer 1

By Euclid’s lemma,

3000 = 525 × 5 + 375  .......[∵ Dividend = Divisor x Quotient + Remainder]

525 = 375 × 1 + 150 

375 = 150 × 2 + 75 

150 = 75 × 2 + 0

∴ HCF (525, 3000) = 75

The numbers 3, 5,15, 25 and 75 divides the numbers 525 and 3000 that means these all are common factors of 525 and 3000.

The highest common factor among these is 75.