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Subject Test Math 1

Question 14 of 32

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SAT Subject Test

What is the least positive integer that has the same number of positive factors as 175?

Select an Answer

8

Correct Answer: 
No

10

Correct Answer: 
No

12

Correct Answer: 
Yes

16

Correct Answer: 
No

18

Correct Answer: 
No

The number 175 is equal to 5 invisible times cross times 5 cross times 7. It has a total of 6 positive factors: 1, 5, 7, 25, 35, and 175. The numbers with 6 positive factors are of the form P subscript 1 end subscript to the power of 2 end exponent invisible times times P subscript 2 end subscript or P to the power of 5 end exponent. The least number of the first form is 2 to the power of 2 end exponent invisible times times 3 invisible times equals 12. The least number of the second form is 2 to the power of 5 end exponent invisible times equals 32. Thus, the answer is 12, which has the 6 positive factors 1, 2, 3, 4, 6, and 12.

You could also test each of the choices, but that may take additional time.

Question Difficulty: 
medium