let a be greatest number that will divide 125 535 and 625 leaving the same reminder in case then then sum of digit a
Answers
Given : a be greatest number that will divide 125 535 and 625 leaving the same reminder
To Find : Sum of Digit of a
Solution:
125 = aX + R
535 = aY + R
625 = aZ + R
=> 535 - 125 = a(X - Y) = 410
625 - 125 = a(Z - X) = 500
625 - 535 = a(Z - Y) = 90
a is greatest number hence a is the HCF of
410 , 500 , 90
500 = 410 * 1 + 90
410 = 90 * 4 + 50
90 = 50 * 1 + 40
50 = 40 * 1 + 10
=> 40 = 10 * 4
10 is the HCF
Hence 10 is the greatest number that will divide 125 535 and 625 leaving the same reminder 5
a = 10
Sum of digits = 1 + 0 = 1
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