The sum of all the factors of 45000 which are exactly the multiples of 10 is
(A) 152295
(B) 141960
(C) 600
(D) 1100
Answers
Given : 45000
To Find : The sum of all the factors of 45000 which are exactly the multiples of 10 is
(A) 152295
(B) 141960
(C) 600
(D) 1100
Solution:
45000 = 2³ * 5⁴ * 3²
Multiples of 10 Hence take away 2 * 5
=> remaining factors = 2² * 3² * 5³
Sum of factors
{(2²⁺¹ - 1)/(2 - 1) } * {( 3²⁺¹ - 1)/(3 - 1) } * { (5³⁺¹ - 1) /( 5 - 1) }
= 7 * 13 * 156
= 14,196
multiple of 10 was taken away hence multiply with that :
14196 * 10 = 141960
Solving by elimination method for given option
the multiples of 10 will end with 0 hence sum will be zero
45000 it self is a multiple of 10
Hence sum must be > 45000
so 600 and 1100 eliminated ,
152295 does not end with 0 hence eliminated
So only option left is 141960
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