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How many distinct positive factors does 30,030 have?

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Re: How many distinct positive factors does 30,030 have?

by Scott@TargetTestPrep » Sun Jul 05, 2020 1:52 pm
BTGModeratorVI wrote: ↑
Sat Jun 27, 2020 6:47 am
 How many distinct positive factors does 30,030 have?

A. 16
B. 32
C. 64
D. 128
E. 256

Answer: C
Solution:

Let’s prime factorize 30,030:

30,030 = 30 x 1001 = 2 x 3 x 5 x 7 x 143 = 2 x 3 x 5 x 7 x 11 x 13

Since 30,030 has 6 distinct prime factors and each prime factor is only raised to the power of 1, then the number of factors that 30,030 has is (1 + 1)^6 = 2^6 = 64.

Answer: C

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