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.
Factors of 4: 1, 2 and 4. Prime Factorization of 4: 2 ×2 or 2^{2}. |
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:
Positive Factors of 4 |
Positive Pair Factors of 4 |
1 × 4 |
(1, 4) |
2 × 2 |
(2, 2) |
Hence, the positive pair factors of 4 are (1, 4) and (2, 2).
Negative Pair Factors of 4:
Negative Factors of 4 |
Negative Pair Factors of 4 |
-1 × -4 |
(-1, -4) |
-2 × -2 |
(-2, -2) |
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 2^{2}.
Video Lesson on Prime Factors
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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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Frequently Asked Questions on Factors of 4
What are the Factors of 4?
The factors of 4 are 1, 2 and 4.
What is the prime factorization of 4?
The prime factorization of 4 is 2 ×2 or 2^{2}.
Write down the positive and negative pair factors of 4.
The positive pair factors of 4 are (1, 4) and (2, 2).
The negative pair factors of 4 are (-1, -4) and (-2, -2).
What is the sum of factors of 4?
The sum of factors of 4 is 7. We know that the factors of 4 are 1, 2 and 4.
Hence, the sum of factors of 4 = 1+2+4.
Is 2 a factor of 4?
Yes, 2 is a factor of 4. If 4 is divisible by 2, it leaves a remainder 0, and hence 2 is a factor of 4.
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