Question

X is the greatest no by which when 2460,2633,2806 are divided in each case same remainder is obtained.What is the sum of digits

Answer 1

Answer:

The sum of digits is 11.

Step-by-step explanation:

Given : The greatest number by which when 2460,2633,2806 are divided in each case same remainder is obtained.

To find : What is the sum of digits ?

Solution :  

First we find the difference between the numbers 2460,2633,2806.

The required numbers are  

2633-2460=173

2806-2633=173

2806-2460=346

Now, We find the HCF of 173 and 346.

$173=1\times 173$

$346=2\times 173$

$HCF(173,346)=173$

The sum of digits is 173=1+7+3=11

Therefore, the sum of digits is 11.

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

X the greatest number by which when 2460,2633,2806 are divided in each case same remainder is obtained

TO DETERMINE

The sum of digits of X

CALCULATION

Let R be the Remainder in each case

Then we can write the given numbers as below

$2460 = aX + R \: \: \: .......(1)$

$2633 = bX + R \: \: \: .......(2)$

$2806 = cX + R \: \: \: .......(3)$

Where a, b, c are the quotient respectively

Now Equation (2) - Equation (1) gives

$(b-a ) X = 173 \: \: \: \:$

Similarly

$(c - b ) X = 173 \: \: \: \:$

$(c - a ) X = 346\: \: \:$

So From above it is clear that

$X = gcd(173 \: 173 \: 346)$

$\implies \: X = 173$

Hence the sum of the digits of X is

$= 1 + 7 + 3$

$= 11$