Question

Using Euclid’s division algorithm, find the HCF of 504 and 288.

• A. 144
• B. 72
• C. 36
• D. 180

Answer 1

The correct option is B 72

On applying Euclid’s algorithm, i.e. dividing 504 by 288, we get:

Quotient = 1, Remainder = 216

Therefore, 504 = 288 × 1 +216

Again on applying Euclid’s algorithm, i.e. dividing 288 by 216, we get:

Quotient = 1, Remainder = 72

Therefore, 288 = 216 × 1 + 72

Again on applying Euclid’s algorithm, i.e. dividing 216 by 72, we get:

Quotient = 3, Remainder = 0

Therefore, 216 = 72 × 3 + 0

Hence, the HCF of 288 and 504 is 72.