Factors of 4 by Prime Factorization & Factor Tree Method (2024)

Factors of 4 are 1, 2, and 4, while factor pairs of 4 are (1, 4), and (2, 2). A factor of a number is an integer that can completely divide a number without leaving any remainder. In this case, factors of 4 are numbers that can completely divide 4. Factors of 4 can be obtained by finding the prime factorization of 4 or integer factorization of the number. Prime factorization is the process of breaking a number down into a set of prime numbers whose product results in the original number.

• Factors of 4 are 1, 2, and 4.
• Negative factors of 4 are -1, -2, and -4.
• Prime factors of 4 is 2.
• Sum of factors of 4 is 7.
• Prime factorization of 4 is \(2\times 2\).

What are Factors of 4?

There are a total of 3 factors of 4 and they are 1, 2 and 4. Here 1 is the smallest and 4 is the largest factor of 4. All these factors are categorized into prime factors, pair factors (both negative and positive) and common factors.

To get all the factors of 4 we simply need to divide 4 by all the numbers less than 4 and check for the numbers that give 0 as the remainder.

\(4\div 1 = 4\) and remainder is 0, Hence 1 is the factor of 4.

\(4\div 2 = 2\) and remainder is 0, Hence 2 is the factor of 4.

\(4\div 3 = 1\) and remainder is 1, Hence 3 is not the factor of 4.

\(4\div 4 = 1\) and remainder is 0, Hence 4 is the factor of 4.

All the factors of 4 are 1, 2, and 4.

Apart from the above mentioned numbers, 4 when divided by any other number gives a remainder other than zero. Also, if we try and get the remainder as zero, the quotient becomes a fraction or a decimal, but not an integer. Let us check the list of all the possible primes, common factors and composite factors of 4.

Prime Factors of 4

Prime Factors of 4 is 2. Prime numbers in mathematics are numbers that have only two factors: 1 and the number itself.

Expressing 4 as the product of primes = \(2\times 2\)

Common Factors of 2 and 4

Common factors of two or more numbers are the numbers that divide both numbers exactly leaving zero as the remainder.

Example: If we are asked to find the common factors of 2 and 4, then

Factors of 2 = 1, and 2.

Factors of 4 = 1, 2, and 4.

So, the common factors of both the numbers are 1 and 2

Therefore, number 1 is the lowest common factor and 2 is the highest common factor.

Common Factors of 4, 8 and 12

For this we need to first find the factors of 4, 8 and 12 and then find the common factor:

Factors of 4: 1, 2, and 4.

Factors of 8: 1, 2, 4, and 8.

Factors of 12: 1, 2, 3, 4, 6, and 12.

Therefore, the common factors of 4, 8 and 12 is 1, 2 and 4. 1 is the least common factor and 4 is the highest common factor of 4, 8 and 12.

Composite Factors of 4

Composite numbers in mathematics are the numbers that have more than two factors. Composite factors of 4 is 4. A number can be classified as prime or composite depending on their divisibility. The number 4 is an even number and so it is divisible by 2. So, we can say that 4 is a composite number and will surely have more than two factors. The composite factors of 4 will include all the factors of 4 other than 1 and 4.

Factor Pair of 4

Factor pairs of 4 are (1, 4), and (2, 2). A factor pair of any number is when a number divides another and the resultant quotient also divides the original number. These quotients and divisors are referred to as factor pairs.

To find the set of all such pairs, we need to start with the number 1 and the number itself, i.e. 4. Then we need to continue the process by taking the other numbers, i.e. 2, 8, and 4. We can finally terminate the process of pair making when no further pairs are possible.

Factor pair of 4 are given below:

\(1\times 4 = 4, hence (1, 4) is a factor pair.

\(2\times 2 = 4, hence (2, 2) is a factor pair.

Hence, all the above mentioned pairs are the factor pairs of 4.

Negative factor pair of 4 are given below:

\(-1\times -4 = 4, hence (-1, -4) is a factor pair.

\(-2\times -2 = 4, hence (-2, -2) is a factor pair.

As the product of two negative integers is positive, so the resultant of each pair of negative outcomes is also positive.

How to Find Factors of 4?

We can find the factors of 4 by using two methods:

• Factors of 4 byPrime factorization
• Factors of 4 byFactor tree method

Factors of 4 by Prime Factorization

In prime factorization of 4, 4 is expressed as the product of its prime factors.

We can find the prime factors of 4 using the below mentioned steps:

Step 1: Using the rules of divisibility we need to determine the smallest prime factor of 4. In our case, it is 2. Now, we divide 4 by 2 and get 2 as a quotient.

Step 2: Now, 2 is itself a prime number.

Step 3: We divide 2 by 2 and get 1 as a quotient.

Step 4: As 1 is not further divisible by any other number, so we stop the process of prime factorization at this point.

On combining the prime factors, we get; 4 = \(2\times 2\) = \(2^2 = 4\).

Factors of 4 by Factor tree method

In this method, we try to break the given number into a set of prime numbers, which when multiplied together, give the original number. The steps to get the factors are:

Step 1: First, select the factor pair with the smallest prime number. Here, we can take it as 2 and pair it up with 2, as 2 multiplied by 2 gives 4.

Step 2: As both the numbers in the last step are prime, i.e. 2 and 2, we will terminate the splitting process. Bringing the prime factors all together, we get 2, and 2. Also, the product of 2, and 2 is equivalent to 4.

Factors of 4 Solved Examples

Example 1: Is 4 a factor of 60?

Ans: Yes, 4 is a factor of 60. Other factors of 60 are 1, 2, 3, 5, 6, 10, 12, 15, 20, 30, and 60.

Example2: Find the common factors of 4, 8 and 12.

Ans: For this we need to first find the factors of 4, 8 and 12 and then find the common factor:

Factors of 4: 1, 2, and 4.

Factors of 8: 1, 2, 4, and 8.

Factors of 12: 1, 2, 3, 4, 6, and 12.

Therefore, the common factors of 4, 8 and 12 is 1, 2 and 4.