let a be greatest number that will divide 125 535 and 625 leaving the same reminder in case then then sum of digit a
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Sum of digit of a is 1
Given:
a is the greatest number that will divide 125 535 and 625 leaving the same remainder in each case.
To find:
Sum of digits of a
Solution:
Firstly we have to find a.
There is a concept that that if we have 3 numbers b, c and d then the greatest number that will divide all three of them leaving the same remainder will be the H.C.F of (c-b), (d-c), (d-b).
So,
b = 125
c = 535
d = 625
(c-b) = 535 - 125 = 410
(d-c) = 625 - 535 = 90
(d-b) = 625 - 125 = 500
Now we have to find H.C.F. of 410,90,500
Using factorisation method,
410 = 2 * 5* 41
90 = 2* 3*3* 5
500 = 2*2*2* 5*5*5
So, the common factors are 2 and 5
H.C.F. = 2*5 = 10
a = 10
Sum of digits of a = 1+0 = 1
Hence, the answer is 1.
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