S11-22 If n is a positive integer, is n divisible by at least six positive integers?
(1) n is the product of three different prime numbers.
(2) n = 30
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Is n dvisible by at least 6 positive integers?
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mehravikas
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mehravikas
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Can you explain with an example please?
From my understanding, statement 1 is insufficient. Let n = 5 i.e. 5 * 3 * 2, in this case n is not divisible by 6 positive integers.
From my understanding, statement 1 is insufficient. Let n = 5 i.e. 5 * 3 * 2, in this case n is not divisible by 6 positive integers.
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Ian Stewart
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If n = 2*3*5, then n is divisible by 1, 2, 3, 5, 6 (=2*3), 10 (=2*5), 15 (=3*5) and 30 (=2*3*5) - eight different positive integers. In fact, if n is equal to the product of three different primes p, q and r, then n = pqr, and n must be divisible by:mehravikas wrote:Can you explain with an example please?
From my understanding, statement 1 is insufficient. Let n = 5 i.e. 5 * 3 * 2, in this case n is not divisible by 6 positive integers.
1, p, q, r, pq, pr, qr, and pqr
All of these numbers must be different, because numbers have unique prime factorizations. Every number that has three distinct prime divisors has at least eight positive divisors. If n = pqr, where p, q and r are different primes, then n has precisely 8 divisors.
So each Statement is sufficient (the second statement is a special case of the first). D.
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mehravikas
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Thanks. I was thinking that divisible by 6 integers means exactly 6.
Ian Stewart wrote:If n = 2*3*5, then n is divisible by 1, 2, 3, 5, 6 (=2*3), 10 (=2*5), 15 (=3*5) and 30 (=2*3*5) - eight different positive integers. In fact, if n is equal to the product of three different primes p, q and r, then n = pqr, and n must be divisible by:mehravikas wrote:Can you explain with an example please?
From my understanding, statement 1 is insufficient. Let n = 5 i.e. 5 * 3 * 2, in this case n is not divisible by 6 positive integers.
1, p, q, r, pq, pr, qr, and pqr
All of these numbers must be different, because numbers have unique prime factorizations. Every number that has three distinct prime divisors has at least eight positive divisors. If n = pqr, where p, q and r are different primes, then n has precisely 8 divisors.
So each Statement is sufficient (the second statement is a special case of the first). D.
