Question

If x is number which when divides 1836, 810, 1296 and 702 leaves the same remainder each time. Find the value of the sum of the digits in x.
1. 642
2. 18
3. 27
4. 9

Answer 1

Correct Answer - Option 4 : 9

Given∶

HCF is number which when divides 1836, 810, 1296 and 702 leaves the same remainder.

Formula Used∶

Concept of HCF, Prime factorization Method, Common Division Method.

Calculation∶

Calculate the difference of all numbers, taking two numbers at a time ∶

1863 – 1296 = 540;

1836 - 810 = 1026;

1836 – 702 = 1134;

1296 – 810 = 486;

1296 – 702 = 594 and

810 – 702 = 108

Now, Find HCF of 540, 1026, 1134, 486, 594 and 108

So, HCF of 540, 1020, 1134, 486, 594 and 108 is 54, which is the required no;

Hence, the sum of the digits in 54 = 5 + 4 = 9

∴ 9 is the required sum of the digits in the greatest number 54.