Question

Look at the following pattern:
$30=2^1\times 3^1\times 5^1$, Total number of factors $(1+1)(1+1)(1+1)=2\times 2\times 2=8$. $30$ is divisible by $8$ factors i.e. $1,2,3,5,6,10,15,30$.
Find the pattern.

Answer 1

If N is a composite number $=a^p\times b^q\times c^r$

Here a, b and c are prime numbers and p, q and r are their power respectively.

Number of factors $=(p+1)(q+1)(r+1)$

Here $30=2^1\times 3^1\times 5^1$

Then number of factor =$(1+1)(1+1)(1+1)=2\times 2\times 2=8$

Then 30 is divisible by 8 factors i.e. $1,2,3,5,6,10,15,30$