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

Solution:

Using the Euclid’s lemma,

3000 = 525 × 5 + 375

We know that

dividend = divisor × quotient + remainder

525 = 375 × 1 + 150

375 = 150 × 2 + 75

150 = 75 × 2 + 0

HCF (525, 3000) = 75.

As 3, 5, 15, 25 and 75 divides 525 and 3000, then all are common factors of 525 and 3000.

Highest common factor is 75

Therefore, the highest common factor among these numbers is 75

✦ Try This: Two positive integers M and n are both divisible by 3, 5, 15, 25 and 75.find the HCF of M and N

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 1

NCERT Exemplar Class 10 Maths Exercise 1.2 Problem 6

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

Summary:

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

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