Question

Make two factor trees of 32.

Answer 1

Hint:
First, we will prime factorize the given number 32 to make trees with different factors. We will then select two DIFFERENT pairs of factors of 32 to mark the beginning of the tree and hence after that we will complete the remaining tree.

Complete step by step solution:
We need to find out the prime factors of 32,

To find the prime factors we need to divide the given number by the smallest prime numbers it is divisible by, hence

Prime factorization of 32 is
 \[ \Rightarrow 32 = 2 \times 16\]
Where,
 \[ \Rightarrow 16 = 2 \times 8\]
Where,
 \[ \Rightarrow 8 = 2 \times 4\]
Where,
 \[ \Rightarrow 4 = 2 \times 2\]

Hence, Using the above equations, we get
 \[ \Rightarrow 32 = 2 \times 2 \times 2 \times 2 \times 2\]

Now for our first-factor tree, we can write 32 as
 \[ \Rightarrow 32 = 2 \times {2^4}\]

The factor tree according to the above factors is

Now for our second-factor tree, we can write 32 as
 \[ \Rightarrow 32 = {2^2} \times {2^3}\]
So we have,
 \[ \Rightarrow 32 = 4 \times 8\]

The factor tree according to the above factors is

Hence, the two figures are the required factor trees.


Note:
Factor trees are the visual representation of factors of a number, though this question is very easy but prime factorization must be done by dividing the minimum prime number possible till the given number is not divisible by any number.