SAT Math Multiple Choice Practice Question 262: Answer and Explanation

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Question: 262

20. If m is the product of all of the integers from 1 to 10, inclusive, and 2ⁿ is a factor of m, then what is the greatest possible value of n?

A. 2
B. 4
C. 8
D. 16
E. 32

Correct Answer: C

Explanation:

You can factor even further in terms of primes: . This shows that there are a maximum of eight factors of 2, so the greatest power of 2 that is a factor of m is 2⁸.

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