Summarize this article:
672 LearnersLast updated on December 16, 2025
Factors of 72
A number that divides another number exactly without leaving any remainder is called a factor. Factors play an important role in many real-life situations, such as determining the best time to schedule work shifts and events.
What are the Factors of 72
Factors of a number often come in pairs, and they can be found using different methods. The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36,72.
The factors of 48 can be written as shown in the table given below:
| Factor Type | Values |
| Positive Factors of 72 | 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 |
| Negative Factors of 72 | −1, −2, −3, −4, −6, −8, −9, −12, −18, −24, −36, −72 |
| Prime Factors of 72 | 2, 3 |
| Prime Factorization of 72 | 2 × 2 × 2 × 3 × 3 = 2³ × 3² |
| The Sum of the Factors of 72 | 195 |
How To Find The Factors of 72?
To find factors, kids can use different methods for easier calculations. A few commonly used methods are as follows -
- Use of Multiplication Method
- Use of Division Method
- Use of Prime Factor and Prime Factorization.
So, here we discuss a detailed explanation of the following methods,
Finding Factors Using Multiplication Method
In this method, we identify pairs of numbers whose product equals the original number. Follow the steps mentioned below to find the factors:
Step 1: Start to multiply with numbers, which gives the value of 72.
Start with 1, and continue to multiply by other numbers.
1 × 72 = 72
2 × 36 = 72
3 × 24 = 72
4 × 18 = 72
6 × 12 = 72
8 × 9 = 72
Step 2: After the calculation, we get to these numbers, the factors of 72.
Step 3: The positive factor pairs of 72 are (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (8, 9)
Step 4: The negative factor pairs of 72 are (-1, -72), (-2, -36), (-3, -24), (-4, -18), (-6, -12), (-8, -9)
Explore Our Programs
Finding Factors Using Division Method
Using this method we will break down the given number until we get the remainder as zero. Let’s follow the steps mentioned below to find the factors of 72:
Step 1: Divide 72 by smaller numbers and see if there is any remainder. E.g., 72/1 = 72.
Step 2: Continue the process by checking other numbers as well. For 72, the factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. Because 72 can be divided evenly by these numbers.
Prime Factors and Prime Factorization
In the method of prime factorization, a number is broken down into the product of its prime factors. The prime factors can be found by following the steps below:
2 is the smallest prime number of 72, so start dividing by 2. Then continue to divide with other prime numbers.
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3÷3 = 1
The prime factorization of 72 is: 72 = 23 × 32
With prime factorization, 72 can be broken down into prime factors, 2 and 3.
Prime Factor of 72
Prime Factorization of 72
Factor Tree
A factor tree is a graphical representation of breaking a composite number into its prime factors. It is an easy method to find out the factors of any number.
Step 1: 72 divided by 2 gives us the quotient 36.
Step 2: Since 36 is not a prime number, it can be divided further.
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷3 = 3
The prime factorization of 72 is written below :
72 =23 × 32
Factor Pairs of 72
The factors of 72 can be written in both positive and negative pairs. The table below represents the factor pairs of 72, where the product of each pair of numbers is equal to 72.
Positive Pair Factors of 72:
| Factors | Positive Pair Factors |
| 1 × 72 = 72 | 1, 72 |
| 2 × 36 = 72 | 2, 36 |
| 3 × 24 = 72 | 3, 24 |
| 4 × 18 = 72 | 4, 18 |
| 6 × 12 = 72 | 6, 12 |
Since the product of two negative numbers is also positive, 72 also has negative pair factors.
Negative Pair Factors of 72:
| Factors | Negative Pair Factors |
| −1 × −72 = 72 | −1, −72 |
| −2 × −36 = 72 | −2, −36 |
| −3 × −24 = 72 | −3, −24 |
| −4 × −18 = 72 | −4, −18 |
| −6 × −12 = 72 | −6, −12 |
| −8 × −9 = 72 | −8, −9 |
Common Mistakes And How To Avoid Them in Factors Of 72
Children tend to make mistakes while finding the factors of a number. Let us look at how to avoid those mistakes.
Mistake 1
Confusing Factors with Multiples
The factors of a number can divide the given number without any remainder, whereas multiples are the products of multiplying the number by an integer. For example for 12, the factors are 1, 2, 3, 4, 6, and 12. And the multiples are 12, 24, and 36, and so on. To avoid this confusion, always understand the concept separately.
Mistake 2
Ignoring the Negative Factors.
Always remember that each positive factor has a corresponding negative factor. For example, factors of 12 are ±1, ±2, ±3, ±4, ±6, ±12.
Mistake 3
Not Checking Divisibility Properly
In some cases, children might assume that a number cannot be divided further. For example, they may assume that 8 isn't a factor of 24. However, this calculation proves otherwise: 24 ÷ 8 = 3 (no remainder). So 8 is a factor of 24. To avoid this error, always check divisibility.
Mistake 4
Avoiding Larger Factors
Sometimes, students may stop the calculation, after identifying the smaller factors, whereas forget to identify the corresponding larger factors. For example: they might list 1, 2, 3, 4, and forget the larger factors 6, 8, 12, and 24. The solution to these mistakes is to divide numbers systematically, and also pair them with larger factors.
Examples on Factors of 72
Problem 1
A pizza slice into 72 slices. If each person gets 6 slices, how many people can be served?
The pizza can serve 12 people.
Explanation
12 people can be served the pizza. To find out how many people can be served, the total number of slices divided by the total number of slices per person :
Number of people = 72 / 6 =12 people.
Problem 2
A classroom hall has 72 seats arranged in rows. If there are 12 rows of seats, how many seats are in each row?
The total number of seats in each row is 6.
Explanation
The hall contains 72 seats arranged in 12 rows, to find the total number of seats in each row, divide by the total number of seats by the number of rows.
Problem 3
GCF of 72 and 24?
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
GCF =24
Explanation
The greatest factor is the number having the highest value 24 is the GCF of 72 and 24.
Problem 4
A Walmart store in Chicago has 72 snack bars for an NFL Sunday event. The manager wants to pack the snack bars into equal bundles so that each bundle has the same number of bars and none are left over. What are all the possible numbers of bundles that can be made?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Explanation
To make equal bundles, the total number of snack bars must be divided evenly.
Any number that divides 72 exactly with no remainder is a factor of 72.
Listing all such numbers gives the possible bundle counts.
Problem 5
A CVS pharmacy in Boston receives 72 tablets of a supplement. The pharmacist needs to prepare equal-sized dosage packs so that each pack contains the same number of tablets and none are left over. What are all the possible numbers of tablets per pack?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Explanation
Each dosage pack must contain a number of tablets that divides 72 evenly.
These numbers are called the factors of 72.
All values that divide 72 without a remainder are valid tablet counts per pack.
Problem 6
A middle school science class in Houston spends $72 on gas (priced per gallon) for a field trip. The teacher wants to split the gas cost equally among students so that everyone pays the same amount with no change left over. How many students could share the cost evenly?
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Explanation
To split $72 evenly, the number of students must divide 72 exactly.
Each number that divides 72 with no remainder is a factor of 72.
These factors represent all possible group sizes that work.
FAQs on Factors of 72
1.What are the smallest and greatest factors of 72?
2.How do you find the GCF of 72 and another number?
3.Can there be negative factors?
4.Is 72 a perfect square?
5.Is 72 divisible by 6?
6.How many factors does 72 have?
7.Which factors of 72 add up to 13?
8.How many even factors does 72 have?
9.What are the odd factors of 72?
10.What is the sum of all the factors of 72?
Important Terms Related to Factors of 72
- Factors: Factors are numbers that divide a given number exactly, without any remainder. For example, 6 is divisible by 1, 2, 3, and 6. Therefore, 1, 2, 3, and 6 are the factors of 6.
- Prime Factors: Prime factors of the numbers that multiply together to give a certain product. For 72, the prime factors are 2 and 3.
- Multiples: We get multiples when we multiply a number by another number. Let’s take some multiples of 2 (2, 4, 6, and so on).
- Composite Numbers: composite numbers are the numbers that have more than 2 factors. For example: The composite number of 10 is 1, 2, 5, and 10
- Negative Factors: These numbers are the negative counterparts of the positive factors of a number. For example: the negative factor of 10 is -1, -2, -5, -10.
More topics related to Factors of 72
![Important Math Links Icon]()
Topics commonly learned together
![Important Math Links Icon]()
Other topics in Factors
![Important Math Links Icon]()
Explore More Numbers Topics
![Important Math Links Icon]()
Numbers category quick links
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.
