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A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the

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A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the

by BTGmoderatorDC » Thu Jun 23, 2022 7:35 pm

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A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two digit prime saturated integer ?

A. 99
B. 98
C. 97
D. 96
E. 95


OA D

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Re: A number is said to be prime saturated if the product of all the different positive prime factors of n is less than

by Ian Stewart » Tue Jun 28, 2022 11:02 am
The root of each answer choice is less than 10, so we're looking for an answer choice which has distinct prime factors that multiply to something less than 10. But the only two distinct primes that multiply to something less than 10 are 2 and 3, so we want the answer that is only divisible by 2 and 3, and the answer must be 96.
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