130 LearnersLast updated on May 26th, 2025
Factors of 252
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 252, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 252?
The numbers that divide 252 evenly are known as factors of 252.
A factor of 252 is a number that divides the number without remainder.
The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, and 252.
Negative factors of 252: -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -28, -36, -42, -63, -84, -126, and -252.
Prime factors of 252: 2, 3, and 7.
Prime factorization of 252: 2² × 3² × 7.
The sum of factors of 252: 1 + 2 + 3 + 4 + 6 + 7 + 9 + 12 + 14 + 18 + 21 + 28 + 36 + 42 + 63 + 84 + 126 + 252 = 768.
How to Find Factors of 252?
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 252. Identifying the numbers which are multiplied to get the number 252 is the multiplication method.
Step 1: Multiply 252 by 1, 252 × 1 = 252.
Step 2: Check for other numbers that give 252 after multiplying
2 × 126 = 252
3 × 84 = 252
4 × 63 = 252
6 × 42 = 252
7 × 36 = 252
9 × 28 = 252
12 × 21 = 252
14 × 18 = 252
Therefore, the positive factor pairs of 252 are: (1, 252), (2, 126), (3, 84), (4, 63), (6, 42), (7, 36), (9, 28), (12, 21), (14, 18). For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the 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 the simple division method -
Step 1: Divide 252 by 1, 252 ÷ 1 = 252.
Step 2: Continue dividing 252 by the numbers until the remainder becomes 0.
252 ÷ 1 = 252
252 ÷ 2 = 126
252 ÷ 3 = 84
252 ÷ 4 = 63
252 ÷ 6 = 42
252 ÷ 7 = 36
252 ÷ 9 = 28
252 ÷ 12 = 21
252 ÷ 14 = 18
Therefore, the factors of 252 are: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.
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 252 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
252 ÷ 2 = 126
126 ÷ 2 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
The prime factors of 252 are 2, 3, and 7.
The prime factorization of 252 is: 2² × 3² × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 252 is divided by 2 to get 126.
Step 2: Now divide 126 by 2 to get 63.
Step 3: Then divide 63 by 3 to get 21.
Step 4: Divide 21 by 3 to get 7.
Here, 7 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 252 is: 2² × 3² × 7.
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 252: (1, 252), (2, 126), (3, 84), (4, 63), (6, 42), (7, 36), (9, 28), (12, 21), (14, 18).
Negative factor pairs of 252: (-1, -252), (-2, -126), (-3, -84), (-4, -63), (-6, -42), (-7, -36), (-9, -28), (-12, -21), (-14, -18).
Common Mistakes and How to Avoid Them in Factors of 252
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the 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 252, 1 and 252 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 252 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 252/1.5 = 168, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 252 are prime numbers.
For example, 2, 3, and 7 are the prime factors of 252, but it has other factors like 4, 12.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 252 as 2² × 3² × 7 and missing all the key factors.
Factors of 252 Examples
Problem 1
There are 9 students and 252 candies. How will they divide it equally?
They will get 28 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of students.
252/9 = 28
Problem 2
A rectangular garden has a length of 14 meters and the total area is 252 square meters. Find the width.
18 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
252 = 14 × width
To find the value of width, we need to shift 14 to the left side.
252/14 = width
Width = 18.
Problem 3
There are 21 gift bags and 252 chocolates. How many chocolates will be in each bag?
Each bag will have 12 chocolates.
Explanation
To find the chocolates in each bag, divide the total chocolates with the bags.
252/21 = 12
Problem 4
In a class, there are 252 students, and 7 groups. How many students are there in each group?
There are 36 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
252/7 = 36
Problem 5
252 books need to be arranged in 6 shelves. How many books will go on each shelf?
Each of the shelves has 42 books.
Explanation
Divide total books with shelves.
252/6 = 42
FAQs on Factors of 252
1.What are the factors of 252?
2.Mention the prime factors of 252.
3.Is 252 a multiple of 9?
4.Mention the factor pairs of 252?
5.What is the square of 252?
6.How can children in United States use numbers in everyday life to understand Factors of 252?
7.What are some fun ways kids in United States can practice Factors of 252 with numbers?
8.What role do numbers and Factors of 252 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 252 skills?
Important Glossaries for Factors of 252
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 252.
- 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 252 are (1, 252), (2, 126), etc.
- Prime factorization: Expressing a number as a product of its prime factors. For example, 252 = 2² × 3² × 7.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, 14 × 18 = 252.
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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.
