Question

What are all the factor pairs of 32?

Answer 1

Hint: To obtain the pair factors of 32 firstly we will find all the factors of 32 by checking which all numbers divide 32 completely. Then we will check on multiplying which two factors together we are getting number 32 back and form a pair of them and get our desired answer.

Complete step by step solution:
To get the factor pair of 32 we will firstly find the factor of 32 as:
$\begin{align}
  & 32\div 1=32 \\
 & 32\div 2=16 \\
 & 32\div 4=8 \\
 & 32\div 8=4 \\
 & 32\div 16=2 \\
 & 32\div 32=1 \\
\end{align}$
In the above case the remainder for each division is 0 that is the number is completely divided by the factors.
So we get the factors of 32 as below:
$1,2,4,8,16,32$
Now, we will check which of the two factors written above when multiplied gives 32 as an answer.
So we can see that
$\begin{align}
  & 1\times 32=32 \\
 & 2\times 16=32 \\
 & 4\times 8=32 \\
 & 8\times 4=32 \\
 & 16\times 2=32 \\
 & 32\times 1=32 \\
\end{align}$
So from above we get our pairs as: $\left( 1,32 \right),\left( 2,16 \right),\left( 4,8 \right),\left( 8,4 \right),\left( 16,2 \right),\left( 32,1 \right)$
In the above three pairs are repeated where the numbers are the same just their position is different inside the bracket.

Hence we can write the factor pairs of 32 as $\left( 1,32 \right),\left( 2,16 \right),\left( 4,8 \right)$.

Note: The term factors used in the solution are the numbers which divide the given number completely without leaving any remainder behind. A positive integer has more than two factors except for the prime numbers which have only two factors that is 1 and the number itself. When two numbers in a pair are multiplied to give a new number then that pair of numbers is known as the factor pair of the number obtained the factor pair is always repeated twice as the position of the two numbers in the pair can be interchange but we still get the same result.