Question

Two buckets contain 546 and 764 liters of water respectively. What will be maximum capacity of container which can measure the water of either buckets exact number of times?

(a) 108

(b) 54

(c) 34

(d) 456

The question was posed to me in an interview for job.

Enquiry is from Real Numbers topic in division Real Numbers of Mathematics – Class 10

Answer 1

Right choice is (a) 108

For explanation: The two buckets contain 546 and 764 liters of water.

546 can be factorized as 2 × 2 × 3 × 3 × 3 × 5 and 764 as 2 × 2 × 3 × 3 × 3 × 7.

To find the maximum capacity of the container which can measure the water of either buckets exact number of times, we have to find the HCF of the two numbers.

HCF of 546 and 764 = 2^2 × 3^3=108

Hence, the maximum capacity of the container is 108 liters.