My Math Forum Is there a way to find the positive integers with 4 factors less than 100?

 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 December 18th, 2016, 06:43 AM #11 Senior Member   Joined: Apr 2008 Posts: 194 Thanks: 3 Thanks again for your excellent solution, romsek.
 January 9th, 2017, 10:15 PM #12 Member     Joined: Oct 2016 From: labenon Posts: 33 Thanks: 4 Here's the number theory approach! You must know that there are 25 primes less than 100 and they are: 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | 97 (25 primes) For a number N to have exactly four factors (divisors), the number should be of the form N = p³ or pq where p and q are distinct prime numbers. Case 1: N =p³ form Clearly, p can acquire only 2 values: 2 and 3 So, there are a total of 2 numbers of the form N =p³. Case 2: N =pq form such that q>p When p=2, 0
January 21st, 2017, 05:12 PM   #13
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The problem is:

Quote:
 Is there a way to find the positive integers with 4 factors less than 100?
I understand this to mean:

Quote:
 Is there a way to find the positive integers with 4 factors each of which is less than 100?
So why are we adding the factors up? Do you understand it to mean the the sum of the factors must be less than 100?

 Tags 100, factors, find, integers, positive, positives

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