101 LearnersLast updated on May 26th, 2025
Factors of 428
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 428, how they are used in real life, and tips to learn them quickly.
What are the Factors of 428?
The numbers that divide 428 evenly are known as factors of 428.
A factor of 428 is a number that divides the number without remainder.
The factors of 428 are 1, 2, 4, 107, 214, and 428.
Negative factors of 428: -1, -2, -4, -107, -214, and -428.
Prime factors of 428: 2 and 107.
Prime factorization of 428: 2² × 107.
The sum of factors of 428: 1 + 2 + 4 + 107 + 214 + 428 = 756
How to Find Factors of 428?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 428. Identifying the numbers which are multiplied to get the number 428 is the multiplication method.
Step 1: Multiply 428 by 1, 428 × 1 = 428.
Step 2: Check for other numbers that give 428 after multiplying
2 × 214 = 428
4 × 107 = 428
Therefore, the positive factor pairs of 428 are: (1, 428), (2, 214), (4, 107).
All these factor pairs result in 428.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 428 by 1, 428 ÷ 1 = 428.
Step 2: Continue dividing 428 by the numbers until the remainder becomes 0.
428 ÷ 1 = 428
428 ÷ 2 = 214
428 ÷ 4 = 107
Therefore, the factors of 428 are: 1, 2, 4, 107, 214, 428.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 428 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
428 ÷ 2 = 214
214 ÷ 2 = 107
107 ÷ 107 = 1
The prime factors of 428 are 2 and 107.
The prime factorization of 428 is: 2² × 107.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 428 is divided by 2 to get 214.
Step 2: Now divide 214 by 2 to get 107.
Step 3: 107 is a prime number and cannot be divided further.
So, the prime factorization of 428 is: 2² × 107.
Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pairs of 428: (1, 428), (2, 214), (4, 107).
Negative factor pairs of 428: (-1, -428), (-2, -214), (-4, -107).
Common Mistakes and How to Avoid Them in Factors of 428
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 428, 1 and 428 are also factors.
Factors of 428 Examples
Problem 1
A farmer has 428 apples and wants to distribute them equally among 4 baskets. How many apples will each basket contain?
Each basket will contain 107 apples.
Explanation
To divide the apples equally, we need to divide the total apples by the number of baskets.
428/4 = 107
Problem 2
A piece of fabric is 428 meters long and needs to be cut into 2 equal parts. How long will each piece be?
214 meters.
Explanation
To find the length of each piece, we divide the total length by the number of pieces.
428/2 = 214
Problem 3
A group of 107 students is sharing 428 pencils equally. How many pencils will each student get?
Each student will get 4 pencils.
Explanation
To find the pencils each student will get, divide the total pencils by the number of students.
428/107 = 4
Problem 4
A company has 428 light bulbs and needs to package them in boxes, each containing 2 bulbs. How many boxes are required?
214 boxes are required.
Explanation
Dividing the total bulbs by the number of bulbs per box gives the number of boxes.
428/2 = 214
Problem 5
A library needs to organize 428 books into sections of 4 shelves. If each shelf holds the same number of books, how many books will each shelf contain?
Each shelf will contain 107 books.
Explanation
Divide the total number of books by the number of shelves.
428/4 = 107
FAQs on Factors of 428
1.What are the factors of 428?
2.Mention the prime factors of 428.
3.Is 428 a multiple of 4?
4.Mention the factor pairs of 428.
5.What is the square of 428?
6.How can children in Canada use numbers in everyday life to understand Factors of 428?
7.What are some fun ways kids in Canada can practice Factors of 428 with numbers?
8.What role do numbers and Factors of 428 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 428 skills?
Important Glossaries for Factors of 428
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 428 are 1, 2, 4, 107, 214, and 428.
- Prime factors: The factors which are prime numbers. For example, 2 and 107 are prime factors of 428.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 428 are (1, 428), (2, 214), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, 428 can be expressed as 2² × 107.
- Multiple: A multiple of a number is the product of that number and an integer. For example, 428 is a multiple of 4.
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About BrightChamps in Canada
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
