100 LearnersLast updated on May 26th, 2025
Factors of 9972
Factors are the numbers that divide any given number evenly without a 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 9972, how they are used in real life, and tips to learn them quickly.
What are the Factors of 9972?
The numbers that divide 9972 evenly are known as factors of 9972.
A factor of 9972 is a number that divides the number without a remainder.
The factors of 9972 are 1, 2, 3, 4, 6, 12, 831, 1662, 2493, 3324, 4986, and 9972.
Negative factors of 9972: -1, -2, -3, -4, -6, -12, -831, -1662, -2493, -3324, -4986, and -9972.
Prime factors of 9972: 2, 3, and 277.
Prime factorization of 9972: 2² × 3² × 277.
The sum of factors of 9972: 1 + 2 + 3 + 4 + 6 + 12 + 831 + 1662 + 2493 + 3324 + 4986 + 9972 = 23304
How to Find Factors of 9972?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 9972. Identifying the numbers which are multiplied to get the number 9972 is the multiplication method.
Step 1: Multiply 9972 by 1, 9972 × 1 = 9972.
Step 2: Check for other numbers that give 9972 after multiplying
2 × 4986 = 9972
3 × 3324 = 9972
4 × 2493 = 9972
6 × 1662 = 9972
12 × 831 = 9972
Therefore, the positive factor pairs of 9972 are: (1, 9972), (2, 4986), (3, 3324), (4, 2493), (6, 1662), (12, 831).
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 a simple division method:
Step 1: Divide 9972 by 1, 9972 ÷ 1 = 9972.
Step 2: Continue dividing 9972 by the numbers until the remainder becomes 0.
9972 ÷ 1 = 9972
9972 ÷ 2 = 4986
9972 ÷ 3 = 3324
9972 ÷ 4 = 2493
9972 ÷ 6 = 1662
9972 ÷ 12 = 831
Therefore, the factors of 9972 are: 1, 2, 3, 4, 6, 12, 831, 1662, 2493, 3324, 4986, 9972.
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 9972 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
9972 ÷ 2 = 4986
4986 ÷ 2 = 2493
2493 ÷ 3 = 831
831 ÷ 3 = 277
277 ÷ 277 = 1
The prime factors of 9972 are 2, 3, and 277.
The prime factorization of 9972 is: 2² × 3² × 277.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 9972 is divided by 2 to get 4986.
Step 2: Now divide 4986 by 2 to get 2493.
Step 3: Then divide 2493 by 3 to get 831.
Step 4: Divide 831 by 3 to get 277.
Here, 277 is the smallest prime number, that cannot be divided further.
So, the prime factorization of 9972 is: 2² × 3² × 277.
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 9972: (1, 9972), (2, 4986), (3, 3324), (4, 2493), (6, 1662), and (12, 831).
Negative factor pairs of 9972: (-1, -9972), (-2, -4986), (-3, -3324), (-4, -2493), (-6, -1662), and (-12, -831).
Common Mistakes and How to Avoid Them in Factors of 9972
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 9972, 1 and 9972 are also factors.
Factors of 9972 Examples
Problem 1
A group of 831 students is to be divided into equal sections for a field trip. How many sections can be made if each section has 12 students?
69 sections.
Explanation
To divide the students equally, we need to divide the total number of students by the number of students per section.
831/12 = 69
Problem 2
A rectangular garden has a length of 277 meters and a total area of 9972 square meters. What is the width of the garden?
36 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
9972 = 277 × width
To find the value of width, divide 9972 by 277.
9972/277 = width
Width = 36.
Problem 3
A bakery produces 1662 loaves of bread and wants to pack them into boxes containing 6 loaves each. How many boxes are needed?
277 boxes.
Explanation
To find the number of boxes, divide the total loaves of bread by the number of loaves per box.
1662/6 = 277
Problem 4
A company has 3324 products to be divided equally among 3 warehouses. How many products will each warehouse receive?
1108 products.
Explanation
Dividing the products by the total number of warehouses, we will get the number of products in each warehouse.
3324/3 = 1108
Problem 5
There are 4986 candies to be evenly distributed among 831 children. How many candies will each child receive?
Each child will receive 6 candies.
Explanation
Divide total candies by the number of children.
4986/831 = 6
FAQs on Factors of 9972
1.What are the factors of 9972?
2.Mention the prime factors of 9972.
3.Is 9972 a multiple of 4?
4.Mention the factor pairs of 9972?
5.What is the square of 9972?
6.How can children in United Arab Emirates use numbers in everyday life to understand Factors of 9972?
7.What are some fun ways kids in United Arab Emirates can practice Factors of 9972 with numbers?
8.What role do numbers and Factors of 9972 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve Factors of 9972 skills?
Important Glossaries for Factor of 9972
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 9972 are 1, 2, 3, 4, 6, 12, 831, 1662, 2493, 3324, 4986, and 9972.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 277 are prime factors of 9972.
- Prime factorization: The expression of a number as a product of its prime factors. For example, 9972 = 2² × 3² × 277.
- 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 9972 are (1, 9972), (2, 4986), etc.
- Multiple: A number that can be divided by another number without a remainder. For example, 9972 is a multiple of 4.
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About BrightChamps in United Arab Emirates
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.
