Question

find the value of a+b+c if 673a is divisible by 15 673b is divisible by 7 and 673c is divisible by 33

Answer 1

given,

673a is divisible by 15. it means, 673a is divisible by 3 and 5.

from divisibility test of 3 : (6 + 7 + 3 + a ) is divisible by 3.

a = 2, 5, ...

from divisibility test of 5 : a = 0 or, 5

so, a = 5.

again, 673b is divisible by 7. it is possible only when b = 4

673c is divisible by 33. it means, 673c is divisible by 11 and 3.

from divisibility test of 3 : (6 + 7 + 3 + c) is divisible by 3.

so, c = 2, 5, ...

from divisibility test of 11 : 6 + 3 - (7 + c) = integral multiple of 11.

or, 9 - 7 - c = 11n , where n is integer.

if we take n = 0

so, c = 2.

now we have, a = 5, b = 4 and c = 2

so, (a + b + c) = 5 + 4 + 2 = 11