Question

What is the highest common factor of 240 and 1500

Answer 1

There are several process for finding the HCF or Highest Common factor for any numbers given. In this case the two numbers given are 240 and 1500.
Firstly we need to divide 1500 by 240 and check if there are any remainders. On dividing we get quotient is 6 and remainder is 60. Now again we have to divide 240 by 60 which we found as remainder previously. Then on dividing 240 by 60 we get no remainder. So the 60 is the HCF or the Highest Common Factor of 240 and 1500. This is the easiest process by which the HCF of any set of numbers can be found.

Answer 2

Another way is to express the two numbers as a product of their prime factors.

240 = 2 x 2 x 2 x 2 x 3 x 5

1500 = 2 x 2 x 3 x 5 x 5 x 5

If you pair up a factor of 240 with the same factor of 1500, you find that 2 matches twice, 3 once and 5 once

so HCF = 2 x 2 x 3 x 5 = 60