152 LearnersLast updated on May 26th, 2025
Factors of 972
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 972, how they are used in real life, and tips to learn them quickly.
What are the Factors of 972?
The numbers that divide 972 evenly are known as factors of 972.
A factor of 972 is a number that divides the number without remainder.
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, and 972.
Negative factors of 972: -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, -81, -108, -162, -243, -324, -486, and -972.
Prime factors of 972: 2 and 3.
Prime factorization of 972: 2² × 3â”.
The sum of factors of 972: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 81 + 108 + 162 + 243 + 324 + 486 + 972 = 3,234
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How to Find Factors of 972?
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 972. Identifying the numbers which are multiplied to get the number 972 is the multiplication method.
Step 1: Multiply 972 by 1, 972 × 1 = 972.
Step 2: Check for other numbers that give 972 after multiplying
2 × 486 = 972
3 × 324 = 972
4 × 243 = 972
6 × 162 = 972
9 × 108 = 972
12 × 81 = 972
18 × 54 = 972
27 × 36 = 972
Therefore, the positive factor pairs of 972 are: (1, 972), (2, 486), (3, 324), (4, 243), (6, 162), (9, 108), (12, 81), (18, 54), (27, 36).
All these factor pairs result in 972.
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 972 by 1, 972 ÷ 1 = 972.
Step 2: Continue dividing 972 by the numbers until the remainder becomes 0.
972 ÷ 1 = 972
972 ÷ 2 = 486
972 ÷ 3 = 324
972 ÷ 4 = 243
972 ÷ 6 = 162
972 ÷ 9 = 108
972 ÷ 12 = 81
972 ÷ 18 = 54
972 ÷ 27 = 36
Therefore, the factors of 972 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972.
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 972 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
972 ÷ 2 = 486
486 ÷ 2 = 243
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of 972 are 2 and 3.
The prime factorization of 972 is: 2² × 3â”.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 972 is divided by 2 to get 486.
Step 2: Now divide 486 by 2 to get 243.
Step 3: Then divide 243 by 3 to get 81.
Step 4: Divide 81 by 3 to get 27.
Step 5: Divide 27 by 3 to get 9.
Step 6: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 972 is: 2² × 3â”.
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 972: (1, 972), (2, 486), (3, 324), (4, 243), (6, 162), (9, 108), (12, 81), (18, 54), (27, 36).
Negative factor pairs of 972: (-1, -972), (-2, -486), (-3, -324), (-4, -243), (-6, -162), (-9, -108), (-12, -81), (-18, -54), (-27, -36).
Common Mistakes and How to Avoid Them in Factors of 972
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 word. Always remember to include 1 and the number itself.
For example, in factors of 972, 1 and 972 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 972 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 972/1.5 = 648, 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 972 are prime numbers.
For example, 2 and 3 are the prime factors of 972, but it has other factors like 4, 9.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, not breaking 972 as 2² × 3â” and missing all the key factors.
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Factors of 972 Examples
Problem 1
There are 18 friends and 972 candies. How will they divide it equally?
They will get 54 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
972/18 = 54
Problem 2
A rectangular garden has a length of 27 meters and a total area of 972 square meters. Find the width?
36 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
972 = 27 × width
To find the value of width, we need to shift 27 to the left side.
972/27 = width
Width = 36.
Problem 3
There are 81 gift boxes and 972 candies. How many candies will be in each gift box?
Each gift box will have 12 candies.
Explanation
To find the candies in each gift box, divide the total candies with the gift boxes.
972/81 = 12
Problem 4
In a theater, there are 972 seats and 9 rows. How many seats are there in each row?
There are 108 seats in each row.
Explanation
Dividing the seats by the total rows, we will get the number of seats in each row.
972/9 = 108
Problem 5
972 apples need to be arranged in 4 baskets. How many apples will go into each basket?
Each of the baskets has 243 apples.
Explanation
Divide total apples with baskets.
972/4 = 243
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FAQs on Factors of 972
1.What are the factors of 972?
2.Mention the prime factors of 972.
3.Is 972 a multiple of 9?
4.Mention the factor pairs of 972?
5.What is the square of 972?
6.How can children in Qatar use numbers in everyday life to understand Factors of 972?
7.What are some fun ways kids in Qatar can practice Factors of 972 with numbers?
8.What role do numbers and Factors of 972 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 972 skills?
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Important Glossaries for Factors of 972
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, and 972.
- Prime Factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 972.
- 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 972 are (1, 972), (2, 486), etc.
- Prime Factorization: Expressing a number as the product of its prime factors. For instance, 972 can be expressed as 2² × 3â”.
- Multiplication Method: A method to find factors by identifying pairs of numbers that multiply to the original number. For example, the multiplication method finds (1, 972), (2, 486), and so on for 972.
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About BrightChamps in Qatar
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.
