Question

Factors of $675$

Answer 1

Factorising $675$

$\begin{array}{cc}5& 675\\ 5& 135\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$

1. The factors on the left are the prime factors of the given number. Thus the prime factorization of $675=3^3·5^2$
2. Picking different groups of the prime factors and multiplying them gives other composite factors of the number.

We see that,
$$\begin{gathered} 675=1\times \overline{3\times 3\times 3\times 5\times 5}=1\times 675 \\ 675=\overline{1\times 3}\times \overline{3\times 3\times 5\times 5}=3\times 225 \\ 675=5\times \overline{1\times 3\times 3\times 3\times 5}=5\times 135 \\ 675=\overline{1\times 3\times 3}\times \overline{3\times 5\times 5}=9\times 75 \\ 675=\overline{1\times 3\times 5}\times \overline{3\times 3\times 5}=15\times 45 \\ 675=\overline{5\times 5}\times \overline{1\times 3\times 3\times 3}=25\times 27 \end{gathered}$$

Thus, the factors of $675$ are $1,3,5,9,15,25,27,45,75,135,225$ and $675$