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For any positive integer n, n>1, the "length" of n is the [#permalink]
 21 Jan 2012, 07:25
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For any positive integer n, n>1, the "length" of n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 50 is 3, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000. A. 10 B. 9 C. 8 D. 7 E. 6 Thanks!
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Re: Length of an integer [#permalink]
21 Jan 2012, 07:32
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Splendidgirl666 wrote: Hi,
is there a short cut for this question:
For any positive integer n, n>1, the "length" of n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 50 is 3, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000.
1. 10
2. 9
3. 8
4. 7
5. 6
Thanks! Basically the length of an integer is the sum of the powers of its prime factors. For example the length of 24 is 4 because 24=2^3*3^1 --> 3+1=4. Now, to maximize the length of an integer less then 1,000 we should minimize its prime base(s). Minimum prime base is 2: so 2^x<1,000 --> x<10 --> maximum length is 9 for 2^9=512. Note that 2^9 is not the only integer whose length is 9, for example 2^8*3=768<100 also has the length of 8+1=9. Answer: B. Check similar questions to practice: for-any-integer-k-1-the-term-length-of-an-integer-108124.htmlfor-any-positive-integer-n-the-length-of-n-is-defined-as-126740.htmlHope it helps.
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For any positive integer n, n>1, the "length" of n is the number of positive primes ( not necessarily distinct) whose product is n. For example, the length os 50 is 3 since 50 = 2*5*5
Q) What is the greatest possible length of a positive integer less than 1000?
a) 10
b) 9
c) 8
d) 7
e) 6
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Re: PT #10 PS 4 Q 15 [#permalink]
04 Mar 2012, 18:38
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Re: For any positive integer n, n>1, the "length" of n is the [#permalink]
10 Feb 2013, 08:39
To maximize the length you should use the smallest prime number, 2. 2x2x2x2x2x2x2x2x2 = 2^9 = 512; 2^10 = 1024 which is > 1000, so you have to use 2^9. The answer is B.
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Re: For any positive integer n, n>1, the "length" of n is the
[#permalink]
10 Feb 2013, 08:39
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