How many factors of 80 are greater than square_root 80?

No need to find all factors of 80.

\(\sqrt{80}\) is more than 8 and less than 9. So we are asked to find # of factors of 80 which are more than 8.

Now, \(80=16*5=2^4*5\) --> # of factors of 80 is \((4+1)(1+1)=10\) (see below how to find the # of factors of an integer). Out of these 10, following 5 factors are less or equal to 8: 1, 2, 4, 5, and 8. So other 5 factors are more than 8.

Answer: 5.

Finding the Number of Factors of an Integer

First 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.

Hope it helps.