Factors of 4

The factors of 4 are the numbers that divide 4 exactly without leaving any remainder. The factors and the pair factors of 4 can be positive or negative. For example, the pair factors of 4 can be (1, 4) or (-1, -4). If we multiply a pair of negative numbers, such as multiplying -1 and -4, it will result in the original number 4. Here, we are going to discuss what are the factors of 4, pair factors and the prime factors of 4 using the prime factorization method and many solved examples.

Table of Contents:

• What are the Factors of 4?
• Pair Factors of 4
• Factors of 4 by Division Method
• Prime Factorization 4
• Solved Examples
• Practice Questions
• FAQs

What are the Factors of 4?

The numbers that divide 4 exactly without leaving a remainder, then the numbers are the factors of 4. In other words, if we multiply a pair of numbers together, which results in the original number 4, the numbers are the factors of 4. As 4 is an even composite number, it has more than two factors. Thus, the factors of 4 are 1, 2 and 4. Similarly, the negative factors of 4 are -1, -2 and -4. 

Pair Factors of 4

A pair factor of 4 is defined as the pair of numbers, which on multiplication results in 4. The positive and negative pair factors of 4 are given below:

Positive Pair Factors of 4:

Hence, the positive pair factors of 4 are (1, 4) and (2, 2).

Negative Pair Factors of 4:

Therefore, the negative pair factors of 4 are (-1, -4) and (-2, -2).

Factors of 4 by Division Method

In the division method, the factors of 4 are found by dividing the number 4 by different integer numbers. The integers divide 4 exactly and leave a remainder 0 are the factors of 4. Now, let us discuss how to find the factors of 4 using the division method.

• 4/1 = 4 (Factor is 1 and Remainder is 0)
• 4/2 = 2 (Factor is 2 and Remainder is 0)
• 4/4 = 1 (Factor is 4 and Remainder is 0)

If any numbers other than 1, 2, and 4 divides 4, it leaves a remainder. Hence, the factors of 4 are 1, 2 and 4.

Prime Factorization of 4

The process of writing the number 4 as the product of its prime factors is called the prime factorization of 4. Go through the following procedure to find the prime factors of 4.

Consider a pair factor of 4, say (1, 4)

Here, number 1 cannot be split further. Now take the other factor, say “4”.

We know that the number 4 is an even composite number and it can be further factored as the product of 2 and 2. 

Hence, 4 can be written as  2 ×2.

Therefore, the prime factorization of 4 is 2 ×2 or 2².

Solved Examples

Example 1:

Find the common factors of 4 and 3.

Solution:

The factors of 4 are 1, 2 and 4.

The factors of 3 are 1 and 3.

As 3 is a prime number, the common factor of 4 and 3 is 1.

Example 2:

Find the common factors of 4 and 5.

Solution:

Factors of 4 = 1, 2 and 4.

Factors of 5 = 1 and 5.

As 5 is a prime number, the common factor of 4 and 5 is 1.

Example 3:

Find the common factors of 4 and 8.

Solution:

The factors of 4 are 1, 2 and 4.

The factors of 8 are 1, 2, 4 and 8.

Hence, the common factors of 4 and 8 are 1, 2 and 4.

Practice Questions

1. Find the common factors of 4 and 16?

2. What is the least common factor of 4 and 8?

3. What is the greatest common factor of 4 and 8?

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