Hello all,
I really hate these types of problems. They seem easy, yet I always have problems with them. I got this one right but it was mainly thanks to guessing.
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If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?
A) 10
B) 11
C) 12
D) 13
E) 14
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*** Answer should be 11 ***
Multiples of numbers
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[quote="adi"]Hello all,
I really hate these types of problems. They seem easy, yet I always have problems with them. I got this one right but it was mainly thanks to guessing.
----------------------------------
If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?
A) 10
B) 11
C) 12
D) 13
E) 14
----------------------------------
*** Answer should be 11 ***[/quote]
This one sounds easy if you think this way:
prime factors of 990 = 11 * 3 * 3 * 5 * 2
which means that 11 has to be in the list of number from 1 to n (since 990 is a factor of product of all integers from 1 to n)
hence the least possible value for n = 11
Hope this makes sense.
I really hate these types of problems. They seem easy, yet I always have problems with them. I got this one right but it was mainly thanks to guessing.
----------------------------------
If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n?
A) 10
B) 11
C) 12
D) 13
E) 14
----------------------------------
*** Answer should be 11 ***[/quote]
This one sounds easy if you think this way:
prime factors of 990 = 11 * 3 * 3 * 5 * 2
which means that 11 has to be in the list of number from 1 to n (since 990 is a factor of product of all integers from 1 to n)
hence the least possible value for n = 11
Hope this makes sense.
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For this question, why just because 11 is a multiple of 990 does this mean that the product of all integers from 1 to 11 (or 11!) is a multiple of 990.
For an example, 5 is a prime factor of 25, but 5! is not a multiple of 25?
Thanks!
Eric
For an example, 5 is a prime factor of 25, but 5! is not a multiple of 25?
Thanks!
Eric
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- Ian Stewart
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Again, look at the prime factorization of 990:[email protected] wrote:For this question, why just because 11 is a multiple of 990 does this mean that the product of all integers from 1 to 11 (or 11!) is a multiple of 990.
For an example, 5 is a prime factor of 25, but 5! is not a multiple of 25?
Thanks!
Eric
990 = 2*3^2*5*11
Since 11! is divisible by 2, 3^2, 5 and 11, 11! is divisible by 990.
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