Question

The greatest integer that divides $358,376$ and $232$. The same remainder in each case is

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

Answer: (D)

$9$

If the remainder is the same in each case and the remainder is not given, HCF of the differences of the numbers is the required greatest number

Given: The greatest number that will divide 358,376 and 232 leaving the same remainder in each case.

To find: The number?

Solution :

First, we find the difference between these numbers.

The required numbers are

376 - 232 = 144

376-358= 18

358 - 232 =126

Now, We find the HCF of 18, 126, and 144

$18=2\times 3^2$

$126=2\times 3^2\times 7$

$144=2^4\times 3^2$

$HCF(18,126,144)=2\times 3\times 3$

Therefore, The required largest number is 18.