Question

The largest number which divides 870 and 720 exactly. Does it also divide the sum and difference of the number

Answer 1

Solution -

To find the largest number find the HCF of 870 and 720

HCF of 870 and 720 by Prime factorization method

870 = 2 * 3 * 5 * 29

HCF of 720 

720 = 2 * 2 * 2 * 2 * 3 * 3 * 5

HCF = 2 * 3 * 5 = 30

As 30 is the HCF, the numbers 870 and 720 are divisible by 30. 

Therefore, Sum and difference of the number also divisible by 30.

check - Sum of 870 and 720 = 870 + 720 = 1590, 1590 / 30 = 53

             Difference of 870 and 720 = 870 - 720 = 150, 150 / 30 = 5

Answer 2

Solution :-

First, we have to find the H.C.F. of 870 and 720

H.C.F. of 870 and 720

870 = 2*3*5*29

720 = 2*2*2*2*3*3*5

Common Factors = 2*3*5

H.C.F. = 2*3*5 = 30

So, 30 is the largest number which divides 870 and 720 exactly. It will exactly divide the sum and difference of 870 and 720.

Let us check our answer.

Sum of 870 and 720 = 870 + 720 = 1590

1590/30

Quotient = 53
Remainder = 0

Difference of 870 and 720 = 870 - 720 = 150

150/30

Quotient = 5
Remainder = 0

Sum and difference of 870 and 720 is exactly divisible by its H.C.F.
Hence, our answer is correct