Factors of 4 Using Prime Factorization
What are the Factors of 4?
Given a number such as 4, a natural number that divides 4 without a remainder is called a factor of 4. Additionally, the quotient obtained post the division operation is also a factor of 4.
The factors of 4 are 1, 2 and 4 because all these numbers divide the number 4 evenly.
List of the Factors of 4
As mentioned earlier, divisibility rules and division facts can be used to determine the factors of 4.
Divisor | Is the number a factor of 4? | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of every number. | 1 x 4 = 4 |
2 | Yes, 4 is even. | 2 x 2 = 4 |
3 | No, 4 \(\div\) 3 = 1 R1 | --- |
4 | No, 4 \(\div\) 4 = 1 R0 | 4 x 1 = 4 |
The Prime Factorization of 4
Natural numbers can also be expressed as a product of prime numbers. These prime numbers are known as the prime factors of natural numbers. The process of breaking up a natural number into its prime factors is known as prime factorization.
The prime factorization of 4 can be represented by using a factor tree as shown below.
So, the prime factorization of 4, which is 2 times 2, produces two prime numbers and both of them are 2.
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Factor Pairs of 4
A factor pair of a number is a set of any two factors such that their product is the number itself.
The factor pairs of 4 are (1, 4) and (2, 2).
1 x 4 = 4
2 x 2 = 4
Factors of 4 | Pair factors of 4 |
|---|---|
1 x 4 | (1, 4) |
2 x 2 | (2, 2) |
Solved Factors of 4 Examples
Example 1: Find the number of common factors of 36 and 4.
Solution:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 4: 1, 2 and 4.
So, the common factors of 36 and 4 are 1, 2 and 4.
Hence, 4 and 36 have 3 common factors.
Example 2: On a table, there are 4 soda drinks. Jenny is responsible for distributing the drinks to her two friends equally. What is the total number of drinks that each friend will receive after the distribution?
Solution:
Total number of drinks = 4
Total number of friends = 2
Number of drinks, each friend will get = \(\frac{4}{2}=2\)
So, each friend will get 2 drinks after Jenny distributes the drinks.
Example 3: Is 3 a factor of 4?
Solution:
No, 3 is not a factor of 4. As the number 3 does not divide 4 exactly. It leaves a remainder of 1. So, 3 is not a factor of 4.
Example 4: Which prime factor of 4 has the highest value?
Solution:
The number 4 has a prime factorization of 2 x 2. As a result, the highest prime factor of 4 is 2.
Example 5: What are the factors common between 18 and 4?
Solution:
Factors of 18 are 1, 2, 3, 6, 9, and 18
Factors of 4 are 1, 2 and 4.
So, the common factors of 18 and 4 are 1 and 2.
A number that has more than two factors, 1 and itself, is called a composite number.
The division of any positive number by 1 results in zero as the remainder, and the quotient is the number itself. Hence, 1 is a factor of all positive numbers.
The factors of 4 are 1, 2 and 4.
So, the least factor of 4 is 1 and the greatest factor is 4 itself.
The following are some important properties of factors:
- An exact divisor of a number is called a factor.
- Every number has a factor of one.
- The greatest factor of a number is the number itself.
- The factor should never be greater than the number.