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Difficulty:
95%
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Question Stats:
33% (02:50) correct
67%
(02:48)
wrong
based on 48
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If 1,296 is written as the product of two distinct positive integers greater than 1, how many possibilities are there for the greater of the two integers ?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
08 Aug 2026, 23:55
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Clue : 1296 is a perfect square
09 Aug 2026, 01:50
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I didn't understand the question. Is it asking that out of the two factors, one is greater. So, how many such possible pairs of factors could be?
Regardless, I assumed this and tried to solve it in this way:
On prime factorizing 1296:
\(1296 = 2^4 * 3^4\)
Using 2 as the smaller factor, there are 6 possibilities and using 3 as another smaller factor, there are 5. (Even if we try other smaller factors, one of these possibilities will repeat.)
Hence, total 11.
Regardless, I assumed this and tried to solve it in this way:
On prime factorizing 1296:
\(1296 = 2^4 * 3^4\)
Using 2 as the smaller factor, there are 6 possibilities and using 3 as another smaller factor, there are 5. (Even if we try other smaller factors, one of these possibilities will repeat.)
Hence, total 11.
