Expressing as a product of prime factors

Given the following numbers list down the prime numbers.

1, 2, 20, 5, 23, 0.1, 7, 4, 29, 13, 32

From the given list above, the prime number are 2, 5, 7, 13, 23, 29

We consider the number 36

The number 36 can be expressed as a product of prime factors

using a tree diagram shown below:

The number 2 and 3 are the prime factors of 36 hence 36 = 2 x 2 x 3 x 3

2 x 2 can be written as 2² in short form. Similarly, 3 x 3 can be written as 3²

Therefore 36 = 2² x 3²

The number 2 in 2² is called a power. It shows the number of times the number

has been multiplied by itself.

Similarly the number 2 in 3² is also called a power.

2² is read as "two to power two" and 3² is read as "three to power two". 

When we write 36 = 2² x 3², we say that 36 has been expressed as a product

of prime factor in power form.

Worked out Examples

Express each of the following numbers as a product of its prime factors.

1. 32

2. 72

3. 54

4. 225