Question

Look at the following pattern:
a) $28=2^2\times 7^1$, Total number of factors $(2+1)(1+1)=3\times 2=6$
$28$ is divisible by $6$ factors i.e. $1,2,4,7,14,28$. 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 $28=2^2\times 7^1$

Then number of factor =$(2+1)(1+1)=3\times 2=6$

Then 28 is divisible by 6 factors i,e, 1,2,4,7,14,28