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Factors of 4 are a list of numbers that can be evenly divided into 4. Factors of 4 are those numbers than can divide 4 exactly without leaving any remainder. There are three factors of 4 which are 1, 2, and 4.The prime factorization of 4 is 2 x 2 where 2 is the only prime factor of 4. 4 is a unique number as it is the smallest composite number and the smallest square of a prime number which is 2. The pair factors of 4 are the set of two numbers that give 4 as the product on multiplication with each other. The factors of 2 in pairs are (1, 4) and (2, 2).
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Key Terms: Factors of 4, Remainder, Prime Factorization, Composite Number, Pair Factors, Multiplication, Prime Factor, Prime Number
What are Factors of 4?
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Factors of 4 are integers that divide 4 completely leaving zero as the remainder. If we multiply a pair of numbers together, and they result in the original number 4, the numbers are the factors of 4. 4 is an even composite number which implies that it has more than two factors. There are 3 factors of 4 in total. 1, 2, and 4 are the factors of 4.
Factors of 4: 1, 2, 4
Factors of 4
How to Calculate Factors of 4?
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4 is the smallest composite number which makes it very easy for one to calculate the factors of 4. The factors of 4 can be calculated using two methods which are:
- Division Method
- Prime Factorization Method
The division method and the prime factorization method would give the same number of factors which are 1, 2, and 4.
Factors of 4 by Division Method
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The factors of 4 are found through the division method by dividing the number 4 by different numbers. The numbers that divide 4 exactly and leave the remainder of 0 are the factors of 4.
- 4/1 = 4 (Factor is 1; Remainder is 0)
- 4/2 = 2 (Factor is 2; Remainder is 0)
- 4/4 = 1 (Factor is 4; Remainder is 0)
Any other number than1, 2, and 4 will leave a remainder on dividing 4. Thus, the factors of 4 are 1, 2, and 4.
Read More: HCF
Factors of 4 by Prime Factorization
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Prime Factorization of 4 refers to the process of writing the number 4 as the product of its prime factors. Here are the steps to calculate the factors of 4 through prime factorization:
- Take a pair factor of 4, for instance, (1, 4)
- We know that the number 1 cannot be split further. So, we will take the other number which is 4.
- 4 is an even composite number that can be further factored as the product of 2 and 2.
- Thus, 4 can be written as 2 × 2.
- Now, we can not factorize 2 further. Thus, the prime factorization of 4 is 2 × 2 or 22.
Prime Factorization of 4
Read More: Prime Number Formula
Factors of 4 in Pairs
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Pair Factors of 4 refers to the pair of numbers, which on multiplication together results in 4. The pair factors of 4 can be positive as well as negative. The negative pair factors are also considered as they would give the value of 4 in positive only on multiplication with each other.
Positive Pair Factors of 4
The positive pair factors of 4 are (1, 4) and (2, 2).
| Positive Factors of 4 | Positive Pair Factors of 4 |
|---|---|
| 1 × 4 | (1, 4) |
| 2 × 2 | (2, 2) |
Negative Pair Factors of 4
The negative pair factors of 4 are (-1, -4) and (-2, -2).
| Negative Factors of 4 | Negative Pair Factors of 4 |
|---|---|
| -1 × -4 | (-1, -4) |
| -2 × -2 | (-2, -2) |
Read More: Co Prime Numbers
Solved Examples on Factors of 4
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Example 1: List the common factors of 4 and 3.
Solution: Writing down all the factors of 4 and 3, we get
- Factors of 4: 1, 2, and 4.
- Factors of 3: 1, and 3.
We can see that there is only one common factor of 4 and 3 which is 1.
Example 2: Niyati and her brother made 4 cupcakes for snacks. They want to evenly distribute the cupcakes. How many cupcakes will each of them receive?
Solution: We know that there are 4 cupcakes. It means that in order to distribute them equally among both of them. We need to divide 4 by 2.
4/2 = 2, as 2 is a factor of 2.
Thus, both Niyati and her brother will get two cupcakes.
Read More:
| Related Topics | ||
|---|---|---|
| Relation Between HCF and LCM | Is '1' a Prime Number? | Properties of LCM and HCF |
| Twin Primes | Fundamental Theorem Of Arithmetic | Real Numbers |
Things to Remember
- Factors of 4 are the integers that divide 4 uniformly with zero as the remainder.
- The number 4 has only three factors.
- The factors of 4 are 1, 2, and 4.
- The prime factorization of 4 is 2 x 2.
- 4 is the smallest composite number.
- The factors of 4 in pairs are (1, 4) and (2, 2).
- The sum of the factors of 4 is 7.
Sample Questions
Ques. What are the common factors of 4 and 5? (2 Marks)
Ans. Listing all the factors of 4 and 5, we get,
- Factors of 4: 1, 2, and 4.
- Factors of 5: 1 and 5.
Since 5 is a prime number, the only common factor of 4 and 5 is 1.
Ques. What are the common factors of 4 and 8? (2 Marks)
Ans. Writing down all the factors of 4 and 5, we get
- Factors of 4: 1, 2, and 4.
- Factors of 8: 1, 2, 4, and 8.
Thus, the common factors of 4 and 8 are 1, 2, and 4.
Ques. Which number gives 4 on multiplying with -2? (2 Marks)
Ans. We know that the negative factor pairs of 4 are (-1, -4), (-2, -2)
-2 × -2 = 4
Thus, when -2 is multiplied by -2, the product is given as 4.
Ques. Check whether 8 is a Factor of 4. (2 Marks)
Ans. No, 8 is not a factor of 4 as it is a multiple of 4. 8 is received when 4 is multiplied by the number 2. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, and so on.
Ques. What are the common factors of 48 and 4? (2 Marks)
Ans. The factors of 48 and 4 are
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
- Factors of 4: 1, 2, and 4.
Thus, the factors of 48 which are also the factors of 4 are 1, 2, and 4.
Ques. What are Factors of 4? (2 Marks)
Ans. Factors of 4 are the numbers that divide the number four completely leaving zero as the remainder. Thus, the factors of 4 are 1, 2, and 4.
Ques. Write the prime factorization of 4. (1 Mark)
Ans. The prime factorization of 4 is written as 2 ×2 or 22.
Ques. State the positive and negative pair factors of 4. (2 Marks)
Ans. The positive and negative pair factors of 4 are as follows:
- Positive pair factors of 4: (1, 4) and (2, 2).
- Negative pair factors of 4: (-1, -4) and (-2, -2).
Ques. Calculate the sum of factors of 4. (2 Marks)
Ans. We know that the factors of 4 are 1, 2, and 4, thus,
Sum of factors of 4 = 1 + 2+ 4 = 7
Thus, the sum of the factors of 4 is 7.
Ques. Check if 2 is a factor of 4. (1 Mark)
Ans. Yes, 2 is a factor of 4 as the number 4 is completely divisible by 2, and it leaves a remainder of 0.
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