Which of the following is NOT a factor of 10^2002?

Question

A. 12

B. 25

C. 32

D. 125

E.400

Answer 1

10^2002 is made up of 2002 10's multiplied together

each 10 is 2*5, so there are 2002 2's and 2002 5's

25 is made up of 2 5's, so it's a factor

32 is made up of 5 2's, so it's a factor

125 is made up of 3 5's, so it's a factor

400 is made up of 4 2's and 2 5's, so it's a factor

12 is 2*2*3 and no power of 10 is divisible by 3, so the answer is A)

Answer 2

10²⁰⁰² = [(2)(5)]²⁰⁰² = 2²⁰⁰²5²⁰⁰²

 

25 = 5² is a factor of 10²⁰⁰²

 

32 = 2⁵ is a factor of 10²⁰⁰²

 

125 = 5³ is a factor of 10²⁰⁰²

 

400 = 2⁴5² is a factor of 10²⁰⁰²

 

The answer is (A).