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prime-saturated

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prime-saturated

by arorag » Mon Sep 01, 2008 11:51 am
A positive integer n 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

IMO 96
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Re: prime-saturated

by parallel_chase » Mon Sep 01, 2008 12:10 pm
arorag wrote:A positive integer n 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

IMO 96
99 = 3*11-33
98 = 2*7 -14
97 = prime number itself
96 = 2*3 - 6
95 = 5*19 - 95

only 96 has product of different prime numbers that is less than sqrt96


Hence D.
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