Summarize this article:
1240 LearnersLast updated on December 16, 2025
Factors of 24
Those numbers whose dividend is completely divisible by quotient are factors. The factor of 24 can neither be a decimal nor a fraction.
What are the Factors of 24
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.These are the numbers that can divide 24 completely.
Negative factors of 24:These are the negative counterparts of the positive factors.
Negative factors: -1, -2, -3, -4, -6, -8, -12, -24
Prime factors of 24: Prime factors are the prime numbers when multiplied together give the product
Prime factors of 24: 2 and 3
Prime factorization of 24: Prime factorization involves breaking the number into its prime factors
Expressed as:- 23× 3
sum of the factors of 24: The sum refers to the number we get by adding the factors of the given number.
Sum: 1+ 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60
The factors of 24 can be written as shown in the table given below:
| Factor Type | Values |
| Positive Factors of 24 | 1, 2, 3, 4, 6, 8, 12, 24 |
| Negative Factors of 24 | -1, -2, -3, -4, -6, -8, -12, -24 |
| Prime Factors of 24 | 2, 3 |
| Prime Factorization of 24 | 2 × 2 × 2 × 3 = 2³ × 3 |
| The sum of the Factors of 24 | 60 |
How to Find the Factors of 24
The factors can be found using different methods. These make sure that the factors obtained are correct. Methods to find the factors of 24:
- Multiplication Method
- Division Method
- Prime Factors and Factorization
Finding Factors Using the Multiplication Method
The multiplication method involves finding pairs of numbers when multiplied, giving 24 as the product.
A step-by-step process of finding the factors:
Step 1: Find the possible numbers whose product will give 24.
Step 2: The numbers found should have 24 as the product. These numbers are its factors.
Step 3: Rewrite the particular numbers and pair them.
A list of numbers whose products are 24 is given below:
- 1 × 24 = 24
- 2 × 12 = 24
- 3 × 8 = 24
- 4 × 6 = 24
Explore Our Programs
Finding factors using the Division Method.
The division method finds the numbers that fully divide the given number.
Step-by-step process in division method:
Step 1: Always start dividing the number with 1. Since every number is divisible by 1, both the number and 1 will always be its factors. Example: 24÷1 = 24
Step 2: Move to the next integer and see if the number gets divided completely. Both divisor and quotient are the factors. Example: 24÷2 = 12, 24÷3 = 8 and so on.
Overview of factors of 24 using the division method:
Prime Factors and Prime Factorization
- Multiplying prime numbers to get the given number as their product is called prime factors.
- Prime factorization is the process of breaking down the number into its prime factors.
Prime Factors of 24
To identify the prime factors of 24, we identify the prime numbers whose product results in 24
Prime Factors of 24: 2, 3
Step 1: Start with the smallest prime number 2
24 ÷ 2 =12
12 ÷ 2 = 6
6 ÷ 2 = 3
Step 2: Take the next prime number, which is 3
24÷3 = 8
Prime Factorization of 24
The process of breaking down 24 into prime numbers and expressing them as a product of these is known as prime factorization.
Prime Factorization of 24 is expressed as 23 × 3
Factor Tree for 24:
The prime factorization is visually represented using the factor tree. It helps to understand the process easily.
Factor Pairs of 24
The factors of 24 can be written in both positive and negative pairs. The tables below show the factor pairs of 24, where the product of each pair of numbers is equal to 24.
Positive Pair Factors of 24:
| Factors | Positive Pair Factors |
| 1 × 24 = 24 | 1, 24 |
| 2 × 12 = 24 | 2, 12 |
| 3 × 8 = 24 | 3, 8 |
| 4 × 6 = 24 | 4, 6 |
Since the product of two negative numbers is also positive, 24 also has negative pair factors.
Negative Pair Factors of 24:
| Factors | Negative Pair Factors |
| −1 × −24 = 24 | −1, −24 |
| −2 × −12 = 24 | −2, −12 |
| −3 × −8 = 24 | −3, −8 |
| −4 × −6 = 24 | −4, −6 |
Common Mistakes and How to Avoid Them in Factors of 24
Mistakes can occur while finding the factors. Learn about the common mistakes that can occur. Solutions to solve the common mistakes are given below.
Mistake 1
Skipping prime factors
Since 24 is an even number, it is possible to think that it doesn’t have any prime numbers. Find the pair of numbers that gives 24 as their product. Filter out the prime factors from the pair of numbers
Mistake 2
Including non-factors as factors of 24
Factors of 24 are those numbers that divide 24 completely.
Mistake 3
Checking the factors of 24 inconsistently.
Each factor of 24 should be checked using the multiplication method to make sure that factor pairs give 24 as the product.
Mistake 4
Making calculation Mistake during division
Manually verify the division calculation to ensure that factors divide 24 completely.
Examples on Factors of 24
Problem 1
find Sum of even factors of 24.
Sum is 56
Explanation
Write down the factors. Identify the even factors and add them together.
Even factors of 24 are: 2, 4, 6, 8, 12 and 24
Problem 2
find Greatest common factor of 24 and 12.
12 is the greatest common factor
Explanation
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 12: 1, 2, 3, 4, 6, 12
The greatest factor is the number having the highest value.
Problem 3
A family in Dallas buys 24 snack packs from Costco for an NFL watch party. They want to divide the snack packs equally into gift bags so that each guest gets the same number of snacks and none are left over. What are all the possible numbers of gift bags they can make?
1, 2, 3, 4, 6, 8, 12, 24
Explanation
To divide the 24 snack packs evenly, the number of gift bags must divide 24 without a remainder.
Numbers that divide 24 exactly are called its factors.
Since 24 can be divided evenly by 1, 2, 3, 4, 6, 8, 12, and 24, these are all the possible numbers of gift bags.
Problem 4
A CVS pharmacy in Boston has a bottle containing 24 tablets of a daily vitamin. The tablets need to be packed into equal-sized weekly dose packs with no tablets left over. What are all the possible numbers of tablets that could go into each dose pack?
1, 2, 3, 4, 6, 8, 12, 24
Explanation
Each dose pack must contain a number of tablets that divides 24 evenly.
These numbers are the factors of 24.
Because 24 can be divided exactly by 1, 2, 3, 4, 6, 8, 12, and 24, each of these amounts can be used as a valid dose size.
Problem 5
A middle school class in New York City is planning a science field trip. The total cost for supplies is $24, including tax. The teacher wants to split the cost equally among students so that everyone pays the same amount with no cents left over. How many students could share the cost evenly?
1, 2, 3, 4, 6, 8, 12, 24
Explanation
To split $24 evenly, the number of students must divide 24 without leaving a remainder.
These possible group sizes are the factors of 24.
Since 24 divides evenly by 1, 2, 3, 4, 6, 8, 12, and 24, all of these are valid numbers of students who could share the cost equally.
FAQs on Factors of 24
1. What is the product of factors of 24?
2.State true or false with respect to the factors of 24. (a) 4 is a prime factor (b) There are 8 factors of 24
3.The prime factorization of 24 is expressed as?
4.The sum of the factors of 24?
5.What is the largest factor of 24?
6.How many factors does 24 have?
7.What is the smallest factor of 24?
8.Which factors of 24 add up to 14?
9.How many even factors does 24 have?
10.What are the odd factors of 24?
Important Terms Related to Factors of 24
- Factors: Factors are those numbers that divide the given number without leaving no remainder.
- prime factorization: The prime factorization of numbers involves breaking them down into their prime factors.
- Prime factors: Prime numbers that multiply together to form a given number.
- Least common multiple (LCM): smallest number which is a multiple of the given number.
- Composite number: Number that has at least more than one divisor other than 1 and the number itself.
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.
