tanveer123 wrote:
Hi Bunnuel, can you explain that a positive number with 5 factors should be of the form Q = prime^4 ?? If i have a number with factors such as 2,3,4 the the positive number comes out to be 24 which has 5 factors 1, 2, 3, 4, and 24 itself. Now can you apply the concept of Q = prime^4 to it please ??
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24, so 8 factors.
Below might helps to understand the answer.
Finding the Number of Factors of an IntegerFirst make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.
The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\).
NOTE: this will include 1 and n itself.
Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)
Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.
According to the above, if and only Q=prime^4 it will have (4+1)=5 factors. For example, Q=2^4=16 --> 16 have the following factors: 1, 2, 4, 8, and 16.
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