Factors of 4: Prime Factorization, Methods, Tree, and Examples

Factorization is the process of breaking a larger number into pairs of two smaller numbersFactors of any given number are termed divisors that are entirely divisible. The numbers can be positive and negative, ultimately dividing a given number (m).
Factors of four

Figure 1 – All possible Factors of 4

In this article, we will be finding the factors of 4, primary and secondary techniques used to calculate them, factors pairs of 4, and some solved examples that will help you better understand the concepts introduced.

What Are the Factors of 4?

Factors of number 4 are 1, 2, and 4.

Factors of 4 are referred to as a set of integers that, when divided by the number 4, produce a perfect whole-number quotient, leaving a zero remainder behind.

As the number 4 is completely divisible by 2, and no remainder is obtained, the number 2 is termed as a factor of 4.

How To Calculate the Factors of 4?

You can calculate the factors of number 4 by employing the division method and laws.

There are two primary methods to calculate the factors of the given number (m):

  1. Division Method
  2. Multiplication Method

Also, the two secondary techniques used to evaluate the factors of the given number (m) are:

  1. Prime Factorization
  2. Factor Tree
Let’s begin by applying division laws to get the factors of 4. Firstly, divide 4 by 4 and the universal factor, i.e., 1, such that, \[ \dfrac {4}{1} = 4, r=0 \] \[ \dfrac {4}{4} = 1, r=0 \] The numbers 1 and 4 are regarded as factors of 4 since the remainder of the above division is zero, and the quotient is a perfect whole-number by nature. Go ahead and divide 4 by 2 such that, \[ \dfrac {4}{2} = 2, r=0 \] The above division shows that 2 is the factor of 4 as it is wholly divisible and yields zero as a remainder. Like all other integers, the number 4 has both positive and negative integer factors. The sign is the sole distinction between the two sets of factors. When written as a mathematical symbol, the numbers that include a minus sign in addition to the proposed arithmetical value are known as the four negative factors. The negative factors of number 4 are listed below: Negative Factors of 4 = -1, -2, -4 The positive factors of 4 are given below: Positive Factors of 4 = 1, 2, 4 The factors of 4 can also be found using the rules of multiplication. This can be done by finding the number pairs that, when multiplied, results in the given number. The list of the numbers in pair are given below:

1 x 4 = 4

4 x 1 = 4

Similarly, the other factors can be found as:

2 x 2 = 4

The above multiplication confirms that 1, 2, and 4 are the factors of 4. Fun Facts for factors of 4 are given below:
  • The factors of 4 are also its multiples.
  • The factors of a given number divide it equally. The same goes for number 4.
  • The number 4 is a perfect square of 2.
  • The number 4 is even in nature, but the sum of its factors is an odd number. 

Sum of the factors = 1+2+4 = 7

Did you know that the number 4 is a unique composite number that is also the square of the smallest possible prime number?

Composite Number

A number includes more factors than just the number 1 and itself, which is said to be composite. Just like 4. So, how is the number four unique? Because all numbers smaller than four are prime numbers, it is unique because it seems to be the first composite number that might exist in mathematics.

Factors of 4 by Prime Factorization

Splitting a number into its prime or different prime factors is known as prime factorization. The prime factors of a given number (m) are a group of prime numbers that, when multiplied together in pairs, produce the original number (m) to which they are a factor. In addition to division and multiplication, prime factorization is a popular method for identifying a number’s factors. To identify the prime factors of 4, we will apply the well-known upside-down approach in this case. The mentioned technique is also referred to as the ladder method. It is called the ladder method because the division is shown visually in a ladder-like fashion.
Prime factorization of four

Figure 2 – Prime Factorization of 4

The prime factorization of 4 can also be expressed as the following expression:

2 x 2= 4

Hence, there are prime factors of 4.

Factor Tree of 4

As the name suggests, a factor tree is a visual representation of factors of any number, with each factor represented by a tree branch. It is said that a factor tree is a pictorial depiction of a number’s prime factors. Let’s calculate factors of 4 by splitting the number 4 into its factors that are further broken into their prime factors. Such that:

4 = 2 x 2

The following image shows the factor tree of the number 4:
Factor tree of four

Figure 3 – Factor Tree of 4

Factors of 4 in Pairs

The groups of numbers that make up the pairs of factors are called factor pairs of a number. They are obtained by multiplying the pair of numbers together that provide the same number whose factors are to be determined. The factors of 4 are referred to as the pair factors when the result of their multiplication is the number 4. Fortunately, there are two pairs of factors for the number 4. The pair of factors of the number 4 are represented as:

1 x 4 = 4

Where (1, 4) is a factor pair of 4. The other factor pair can be found as:

2 x 2 = 4

Hence, (2, 2) is also a factor pair of 4. Also, the pair of factors of 4 can be written as,

-1 x -4 = 4

Where (-1, -4) is a factor pair of 4. The negative factor pair can be determined as:

-2 x -2 = 4

Hence, (-2, -2) is also a factor pair of 4. In other words, Factor Pairs of 4 = (1, 4), (2, 2), (-1, -4), (-2, -2)

Factors of 4 Solved Examples

Let’s solve some examples to understand the factors of 4.

Example 1

Harry wants to know which of the following statements are true. Can you help him determine the correct options?
  1. There are a total of 6 factors of 4. 
  2. The negative factor pairs of 4 are, (-1, -4) and (-2, -2).
  3. The number 4 is prime.

Solution

Considering the first statement: Answer = No The list of factors for number 4 is given as follows:

Factors of 4 = 1, 2, 4

The list shows that are three factors of 4 in total. Considering the second statement: Answer = Yes Negative Factor Pairs of 4 = (-1, -4), (-2, -2) Considering the third statement: Answer = No The number 4 is not a prime number as it has three factors. Any number having more than two factors is called a composite number. The following is the list of factors 4:

Factors of 4 = 1, 2, 4

Hence, the number 4 is composite.

Example 2

Alex wants to calculate the average of the factors of 4. Can you help him in finding the correct answer?

Solution

Given that: The factors of 4 are given below:

Factors of 4 = 1, 2, 4

Such that: The average of the set of factors of 4 is achieved by calculating the sum of the above-mentioned factors, divided by the total number of factors proposed in the list. \[ Average = \frac{\text{Sum of factors}}{\text{Total number of factors}} \] Such that, \[ Average = \frac{1+2+4}{3} \]

Average = $\frac{7}{3}$ 

Average = 2.333

Hence, the average of the factors of 4 is 2.333.

Example 3

Charles misplaced the list of factors of 4 and 2 and cannot find their H.C.F. Can you help him in finding the correct answer? 

Solution

The factors of 4 are given below:

Factors of 2 = 1, 2

Factors of 4 = 1, 2, 4

Such that: From the lists, it can be said that the H.C.F (Highest Common Factor) of the factors of 4 and 2 is the number 2, as there is no number greater than 2 that can divide both 2 and 4 and leave a remainder, i.e., zero, behind.

H.C.F = 2

Images/mathematical drawings are created with GeoGebra. 

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