Factors of 28 are 1, 2, 4, 7, 14 and 28. The factors of 28 are the integers, that completely divide 28 without leaving any remainder, and factor pairs are the numbers that produce the result of 28 when multiplied together. In this case, 1, 2, 4, 7, 14, and 28 are the factors of 28 as they completely divide 28 without leaving any remainder. Also, 7 multiplied by 4 will give 28 like; 4 × 7 = 28. So, 7 and 4 are considered as factor pairs of 28.
In this article, we will learn about factors of 28, prime factors of 28, how to find prime factors, and Prime Factorization of 28 in detail.
Table of Content
What are Factors?
Factor is the number that divides another number evenly i.e., without leaving any remainder. They are whole numbers that can be multiplied to obtain a different whole number in the form of the product.
For example, the factors of 30 are the numbers that perfectly divide 30 i.e., 1, 2, 3, 5, 6, 10, 15, and 30 itself.
Factors of 28
The numbers that divide 28 evenly are its factors. They are 1, 2, 4, 7, 14, and 28. The remainder and quotient of 28 divided by any of its factors will both equal 0 and be natural numbers.
All Factors of 28
All factors of 28 are 1, 2, 4, 7, 14 and 28.
Prime Factors of 28
The prime factors of 28 can be calculated as follows:
- Start with the number 28.
- Then, divide 28 by the smallest number 2;
- Repeat this process, until you get the last prime number which will be 7.
Therefore, the prime factorization using the prime factors of 28 was found: 2 × 2 × 7 and prime factors of 28 are 2 and 7.
How to Find Factors of 28?
A number's factors can be found by determining which factor makes the original number entirely divisible or the multiplication of integers to get the number 28. So, various methods are given below to find the factors of 28.
Division Method
By identifying pairs of numbers that are divided to create 28, you can use the division method to get the factors of 28. So, for that, you have to start with the smallest number 2 and divide until you get the quotient as 1. So, Let's see the factor pairs for 28 are as follows:
- 28 ÷ 2 = 14
- 14 ÷ 2 = 7
- 7 ÷ 7 = 1
So finally, we get the quotient as 1, and the factors of 28 are 2, 2, and 7.
Multiplication Method
By identifying pairs of numbers that multiply to create 28, you can use the multiplication method to get the factors of 28. The factor pairs for 28 are as follows:
- 1 × 28 = 28
- 2 × 14 = 28
- 4 × 7 = 28
- 28 × 1 = 28
- 14 × 2 = 28
- 7 × 4 = 28
Therefore, the factors of 28 obtained by the multiplication method are 1, 2, 4, 7, 14, and 28.
Prime Factorization of 28
The representation of 28 as a product of its prime factors is known as its prime factorization.
So, here the prime factors of 28 are; 28 = 2 × 2 × 7
It is clear that 28 has two prime factors 7 and 2.
Factor Tree of 28
The factor tree of 28, will be expressed as the product of prime factors;
- Let's start with the number 28
- After that, Expand the number 28 into two factors 2 and 14.
- Then, 2 will remain as it is, because it's a prime number.
- At last, the expanded number of 14 are 2 and 7.
Factor Pairs of 28
The numbers that multiply together to produce the original number are known as factor pairs of 28. The factor pairs for 28 are: (2,14); and (-4,-7) both pairs of integers will give you the product 28. So, Let's look after the positive factor pairs, and negative factor pairs in expand.
Positive Factor Pair of 28
The positive factor pairs of 28 are the pairs of positive integers that multiply together to give 28. So, the given pairs are;
- 1 × 28 = 28
- 2 × 14 = 28
- 4 × 7 = 28
So, the two positive factor pairs of integers will bring you to 28.
Negative Factor Pair of 28
The negative factor pairs of 28 are the pairs of negative integers that multiply together to give 28. So, the given pairs are;
- -1 × -28 = 28
- -2 × -14 = 28
- -4 × -7 = 28
So, the two negative factor pairs of integers will bring you to 28.
Also, Check
Solved Examples on Factors of 28
Example 1: What is the Sum of all the factors of 28?
Solution:
Let's find the sum of all factors of 28, Therefore the factors of 28 are; 1, 2,4,7,14 and 28.
1 + 2 + 4 + 7 + 14 + 28 = 56
Therefore, the sum of all the factors of 28 is 56.
Example 2: What are the common factors of 14 and 28?
Solution:
The common factors of 14 and 28 are the numbers that can be evenly divided by following integers for finding the factors of 28.
So, Factors of 14: 1, 2, 7, 14
Factors of 28: 1, 2, 4, 7, 14, 28
Therefore, the common factors are 1, 2, 7, and 14.
Example 3: Express 28 as the product of its prime factors.
Solution:
To express 28 as the product of its prime factors. we can use the prime factorization method.
28=2 × 2 × 7
Therefore, the prime factors of 28 are 2, 2 and 7.
Example 4: Find the product of the first five prime numbers and check if it is a factor of 28.
Solution:
The first five prime numbers are 2, 3, 5, 7, and 11.
And the product of these numbers are 2 × 3 × 5 × 7 × 11 = 2310
Now, If we talk about 2310 is a factor of 28. It can't be possible because 2310 is not divisible by 28.
Therefore, the product of the first five prime numbers are not a factor of 28.
Practice Questions on Factors of 28
Q1: What is the product of the factors of 28?
Q2: Write down the positive pair factors of 28.
Q3: Determine if 5 is a factor of 28.
Q4: Is 4 a factor of 28?
Conclusion
Knowing how to find the factors is an important part of basic math that helps in solving many types of problems. Factors help break down numbers into smaller parts, which is useful in various calculations and problem-solving situations. The factors of 28, including 1, 2, 4, 7, 14, and 28, demonstrate how numbers can be divided evenly. Understanding the factors of 28 is a simple yet important concept in mathematics.
