Question 138
Find the greatest number which on dividing 70 and 50 leaves remainders 1 and 4 respectively
Solution
Let the number be A.
As 70 leaves 1 remainder when divided by A, it could be written as: 70 = Ax + 1 where x is the quotient.
Similarly, 50 = Ay + 4.
Subtracting the equations, we get: 20 = A(x - y) - 3 ==> A(x-y) = 23.
23 can be expressed as a product of 2 numbers in only 1 way as 23 is a prime number.
So, A can either be 23 or 1 and the greatest value that A can take is 23.
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