Factors of 4

Factors of 4 are the list of integers that can be evenly divided into 4. Negative factors of 4 are just factors with a negative sign. Did you know, the number 4 is a special number as it is the smallest composite number and the smallest square of a prime number? In this lesson, we will calculate the factors of 4, along with its prime factors, and its factors pairs. We will also solve some examples for a better understanding of the concept.

• Factors of 4: 1, 2, and 4
• Negative Factors of 4: -1, -2 and -4
• Prime Factorization of 4: 4 = 2²

What are Factors of 4?

Let us recall the meaning of the word "factor." A factor is a number that divides the number into equal parts. The factors of 4 are integers that divide 4 without leaving any remainder. For example, 2 is a factor of 4 because 2 divides 4 without any remainder. Interestingly, the quotient is also 2.

Important Notes:

• Fractions and decimals (numbers that are not integers) cannot be the factors of any number.
• When a number is a factor of the given number, then its additive inverse is also a factor of the given number.
  For example, since 2 is a factor of 4, -2 is also a factor of 4.
• 4 is a perfect square and 2² = 4.

How to Calculate the Factors of 4?

Let us learn how to calculate the factors of 4.

• Step 1: Write down the number to be factored, i.e., 4
• Step 2: Find the two numbers whose product gives 4

To find the factors of 4, we will do the following.

• Let's say we consider 2 to be the factor of 4.
• 4 is equal to the square of 2.
• 2 is a prime number. Hence, it can only be factored as 1 and the number itself i.e. 2.
• 4 can be written as, 2 × 2 = 2² = 4

Hence, the factors of 4 are 1, 2, and 4. Explore factors using illustrations and interactive examples:

• Factors of 400 - The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
• Factors of 245 - The factors of 245 are 1, 5, 7, 35, 49, 245
• Factors of 144 - The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
• Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
• Factors of 40 - The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
• Factors of 48 - The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 4 by Prime Factorization

In the process of prime factorization, the number is written as a product of its prime factors. 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 shown below:

Tips and Tricks:

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

• 1 and 4 are always the factors 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

The pair factors of 4 are obtained by writing 4 as a product of two numbers in all possible ways. In each product, both multiplicands are the factors 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 (-1, -4), (-2, -2), and (-4, -1).

FAQs on Factors of 4

What are all the Factors of 4?

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

Which Number has 4 as a Factor?

All the multiples of 4 have 4 as a factor. The multiples of 4 are 4, 8, 12, 16, 20, and so on.

Is 8 a Factor of 4?

No, 8 is not a factor of 4. The multiples of 4 are 4, 8, 12, 16, 20, and so on.

What is the Prime Factor of 4?

The factors of 4 are 1, 2, and 4. 2 is the only prime factor of 4.

What Factors of 48 are also the Factors of 4?

• The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
• The factors of 4 are 1, 2, and 4.

The factors of 48 which are also the factors of 4 are 1, 2, and 4.