Question

Factorise the following numbers into primes.
$\left(i\right)32\text{(ii)}57\left(iii\right)23\text{(iv)}150\text{(v)}216$
$\begin{array}{ccc}\text{(vi)}208& \text{(vi)}765& \text{(viii)}342\end{array}\left(ix\right)377\left(x\right)559$

Answer 1

(i) Given number $32$ and its prime factorization is
$\begin{array}{cc}2& 32\\ 2& 16\\ 2& 8\\ 2& 4\\ & 2\end{array}$
$\therefore 32=2\times 2\times 2\times 2\times 2=2^5$

(ii) Given $57$ and its prime factorization is
$\begin{array}{cc}3& 57\\ & 19\end{array}$
$\therefore 57=3\times 19$

(iii) Given $150$ and its prime factorization is
$\begin{array}{cc}2& 150\\ 5& 75\\ 5& 15\\ & 3\end{array}$
$\therefore 150=2\times 5\times 5\times 3=2\times 5^2\times 3$

(iv) Given number $216$ and its prime factorization
$\begin{array}{cc}2& 216\\ 2& 108\\ 2& 54\\ 3& 27\\ 3& 9\\ & 3\end{array}$
$\therefore 216=2\times 2\times 2\times 3\times 3\times 3=2^3\times 3^3$

(v) Given number $23$ is prime number,
So, its factorization is $23=23\times 1$

(vi) Given number $208$ and its prime factorization is
$\begin{array}{cc}2& 208\\ 2& 104\\ 2& 52\\ 2& 26\\ & 13\end{array}$
$\therefore 208=2\times 2\times 2\times 2\times 13=2^4\times 13$

(vii) Given number $765$ and its prime factorization is
$\begin{array}{cc}5& 765\\ 3& 153\\ 3& 51\\ & 17\end{array}$
$\therefore 765=5\times 3\times 3\times 17=5\times 3^2\times 17$

(viii) Given number $342$ and its prime factorization is
$\begin{array}{cc}2& 342\\ 3& 171\\ 3& 57\\ & 19\end{array}$
$\therefore 342=2\times 3\times 3\times 19=2\times 3^2\times 19$

(ix) Given number $377$ and its prime factorization is
$\begin{array}{cc}13& 377\\ & 29\end{array}$
$\therefore 377=13\times 29$

(x) Given number $559$ and its prime factorization is
$\begin{array}{cc}13& 559\\ & 43\end{array}$
$\therefore 559=13\times 43$