Question

Question No. 45
The greatest number that will divide 242, 634 and 358, leaving the remainders 2, 4 and 8 respectively is:​

Answer 1

Given :

n₁ = 242

n₂ = 634

n₃ = 358

remainder = 2,4,8 respectively

To find :  

The greatest number which divides 242, 634 and 358 leaving the remainder 2,4,8 respectively.  

Solution :  

First, subtract 2 from 242, 4 from 634, and 8 from 358.  

⇒ 242 - 2 = 240  

⇒ 634 - 4 = 630

 ⇒ 358 - 8 = 350

Then find the HCF. To find the HCF first find the prime factorization of both the numbers.  

Prime factorization of 240 = 2 x 2 x 2 x 2 x 3 x 5  

Prime factorization of 630 = 2 x 3 x 3 x 5 x 7

Prime factorization of  350 = 2 x 5 x 5 x 7

Now take out the common factors from all the factorizations.  

⇒ 2, 5

x = 2 × 5

x =  10

HCF = 10

Thus, 10 is the greatest number which will divide 242, 634, and 358 leaving the remainder 2,4 and 8 respectively.