Factors of 4 | With Prime Factorization | Easy Guide

The factors of 4 are Integers that are evenly divisible by 4. Do you know that the number 4 is a special number because it is the smallest composite number and the smallest square of a prime number? Interesting? 

Here we will calculate the factors of 4, along with its prime factors, as well as its factor pairs. 

Factors of 4

(1, 2, 4)

There are only three factors of 4 i.e. 1, 2, and 4 respectively.

Negative Factors of 4

( -1,-2, -4). 

There are three factors of 4 i.e. -1, -2, and -4.

Prime Factorization of 4

We have 2 x 2 = 4 = 2²

What are Factors of 4?

To start finding factors of 4, we must recall the mathematical definition of a “factor”. In simple words, a factor is a number that divides a number into equal parts with zero reminders. Therefore, we can’t consider any fraction as a factor.

We will consider only those integers as the factors of 4 if they have no reminder left when divided by 4. 

When we divide 2 by 4 without any remainder, so 2 is a factor of 4. Interestingly, the quotient is 2 as well.

Important Notes:

• Fractions and decimals (non-integer numbers) cannot be factors of any number.
• Whenever a number is a factor of a given number, its additive inverse is also a factor of the given number.
  In the same way that 2 is a factor of 4, -2 is also a factor of 4.
• 2²  = 4, since 4 is a perfect square.

How to Calculate the Factors of 4?

We will learn how to calculate the factors of 4 now.

First, we make pair of two factors that brings 4 as a product.

Let’s see how we get 4 by multiplying two factors.

• 1 x 4 = 4
• 2 x 2= 4
• 4 x 1= 4

 Since we know that 1 is the primary factor of all numbers and the number itself is 4, so we will consider 2 to be a factor of 4. But when we count it as, how many factors of 4? 

The answer is ( 1, 2, and 4)

• 1 is the primary factor in all numbers
• 4 is the factor of itself because every number is a factor of itself.
• The square of 2 is 4.
• We know that 2 is an  even prime number

Therefore, factors 4 are 1, 2, and 4. 

Factors of -4

When we multiply two numbers, and we get -4 as a product, those numbers are the factors of -4. Here is the explanation:

-1 x  4 = -4

 1 x -4 = -4

 2 x -2 = -4

-2 x  2 = -4

Therefore, the factors of -4 in pairs are ( -1, 4), (1,-4), ( -2, 2). 

Use examples and illustrations to explore the following factors:

Factors of 400

We have factors of 400 as 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200,  and 400.

Factor of 45

1, 3, 5, 9, 15 and 45

Factors of 144

We have factors of 144 i.e.  1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.

Factors of 24

We have factors of 24 that are 1, 2, 3, 4, 6, 8, 12,  and 24.

Factors of 40 

We have factors of 40  that are 1, 2, 4, 5, 8, 10, 20, and 40.

Factors of 5

We have factors of 5. That is 1 and 5.

Factors of 4 by Prime Factorization

To get the prime factorization of 4, we divide it by its smallest prime factor which is 2 which is 4/2 = 2.

Since 2 is a prime number, it is divisible by 2 only. This process goes on till we get the quotient as 1. The prime factorization of 4 is as follows:

Tips and Tricks:

1. While finding the factors of the number 4, keep the following points in your mind:

• 1 is the primary factor of all numbers including 4, the number itself, is always the factor of the number 4.
• To find the other factors of the number 4, we first find its prime factorization. The multiplicands of the prime factorization are the prime factors of the number 4.

Factors of 4 in Pairs

When we multiply two numbers, and they bring 4 as a product, we count them as the factors of 4. Those factors are the pair factor of 4.

It is possible to have negative pair factors as well because the product of two negative numbers gives a positive number.

The negative pair factors of 4 are as follows:

• (-1, -4) = 4
• (-2, -2) = 4
• (-4, -1) = 4

Factors of 4 Solved Examples

FAQs