Question

The product of two numbers is 2560 and their LCM is 320. Find their HCF. By process​

Answer 1

The HCF of two numbers is 8.

Step-by-step explanation:

We are given that the product of two numbers is 2560 and their LCM is 320.

From this we have to find the HCF of two numbers.

As we know that it is stated that;

                 Product of two numbers =  HCF $\times$ LCM

To verify this; let us take two numbers 4 and 6.

LCM of 4 and 6 comes out to be 12.

And for HCF of 4 and 6;

  Factors of 4 = 1, 2, 4

  Factors of 6 = 1, 2, 3, 6

So, the Highest common factor between both of the numbers is 2.

Now,     Product of two numbers =  HCF $\times$ LCM

                        4 $\times$ 6  =  12 $\times$ 2

                            24  =  24

Hence, verified.

Therefore,  2560  =  HCF $\times$ 320

                     HCF  =  $\frac{2560}{320}$  =  8

Hence, the HCF of two numbers is 8.