102 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 items equally, arranging things, etc. In this topic, we will learn about the factors of -252, how they are used in real life, and 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 = 936
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 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 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 step shows:
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 as 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 the 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.
Factors of -252 Examples
Problem 1
There are 18 students and -252 points to be distributed equally. How many points will each student get?
Each student will get -14 points.
Explanation
To distribute the points equally, we need to divide the total points by the number of students.
-252/18 = -14
Problem 2
A rectangular garden has a length of 12 meters and a total area of -252 square meters. What is its width?
-21 meters.
Explanation
To find the width of the garden, use the formula:
Area = length × width
-252 = 12 × width
To find the value of width, shift 12 to the left side.
-252/12 = width
Width = -21
Problem 3
There are 42 packs and -252 chocolates. How many chocolates will be in each pack?
Each pack will have -6 chocolates.
Explanation
To find the chocolates in each pack, divide the total chocolates by the number of packs.
-252/42 = -6
Problem 4
In a class, there are -252 candies and 9 groups. How many candies are there in each group?
There are -28 candies in each group.
Explanation
Dividing the candies by the total groups gives the number of candies in each group.
-252/9 = -28
Problem 5
-252 books need to be arranged in 36 shelves. How many books will go on each shelf?
Each of the shelves will have -7 books.
Explanation
Divide total books by shelves.
-252/36 = -7
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 6?
4.Mention the factor pairs of -252.
5.What is the square of -252?
6.How can children in Saudi Arabia use numbers in everyday life to understand Factors of -252?
7.What are some fun ways kids in Saudi Arabia can practice Factors of -252 with numbers?
8.What role do numbers and Factors of -252 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve Factors of -252 skills?
Important Glossaries for Factor 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, and 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.
- Negative factors: Factors that are negative, dividing the number evenly. For example, -1, -2, -3, -4, etc., are negative factors of -252.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of -252 is 2² × 3² × 7.
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About BrightChamps in Saudi Arabia
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.
