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516 LearnersLast updated on December 16, 2025
Factors of 48
Factors are the numbers that divide a given number evenly without leaving any remainder. In real life, factors are used for equal distribution of items in a group or comparisons, and solving mathematical problems. Let's learn more about factors of 48.
What are the Factors of 48
Factors of a number often come in pairs, and they can be found using different methods. Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
The factors of 48 can be written as shown in the table given below:
| Factor Type | Values |
| Positive Factors of 48 | 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 |
| Negative Factors of 48 | -1, -2, -3, -4, -6, -8, -12, -16, -24, -48 |
| Prime Factors of 48 | 2, 3 |
| Prime Factorization of 48 | 2 × 2 × 2 × 2 × 3 = 2⁴ × 3 |
| Sum of Positive Factors of 48 | 124 |
How to Find the Factors of 48?
To find factors of a number, kids can use different methods for easy 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 with 1 and continue multiplying it with other numbers until you get 48.
Step 2: After the calculation, we get to these numbers, the factors of 48.
1 × 48 = 48
2 × 24 = 48
3 × 16 = 48
4 × 12 = 48
6 × 8 = 48
Step 3: The factor pairs of 48 found through multiplication are (1, 48) (2, 24) (3, 16) (4, 12), and (6, 8)
Step 4: The negative factor pairs of 48 are (-1, -48) (-2, -24) (-3, -16) (-4, -12), and (-6, -8)
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Finding Factors Using Division Method
In the division method, we will break down the given number until we get the remainder as zero. Follow the steps mentioned below to find the factors of 48 by division method:
Step 1: Divide 48 by smaller numbers and see if the remainder is zero. For Example, 48÷1 = 48.
Step 2: Continue the process for other numbers as well. For 48, the factors are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. Because 48 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, so start dividing by 2. And then continue to divide with other prime numbers.
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1
The prime factorization of 48 is :
48 = 24 × 31
Finally, using the prime factorization method, the prime factors of 48 are 2 and 3.
Prime Factors of 48
Prime Factorization of 48
Factor Tree
A factor tree is a graphical representation of breaking down a composite number into its prime factors. It is an easy method to find prime factors of any number.
Step 1: 48 divided by 2 gives us the quotient of 24
Step 2: Since 24 is not a prime number, it can be divided further.
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1
The prime factorization of 48 is written below :
48= 24 × 3.
Factor Pairs of 48
The factors of 48 can be written in both positive and negative pairs.
The table below shows the factor pairs of 48, where the product of each pair of numbers is equal to 48.
Positive Pair Factors of 48:
| Factors | Positive Pair Factors |
| 1 × 48 = 48 | 1, 48 |
| 2 × 24 = 48 | 2, 24 |
| 3 × 16 = 48 | 3, 16 |
| 4 × 12 = 48 | 4, 12 |
| 6 × 8 = 48 | 6, 8 |
Since the product of two negative numbers is also positive, 48 also has negative pair factors.
Negative Pair Factors of 48:
| Factors | Negative Pair Factors |
| −1 × −48 = 48 | −1, −48 |
| −2 × −24 = 48 | −2, −24 |
| −3 × −16 = 48 | −3, −16 |
| −4 × −12 = 48 | −4, −12 |
| −6 × −8 = 48 | −6, −8 |
Common Mistakes and How to Avoid Them in Factors Of 48
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, the factors of 12 are 1, 2, 3, 4, 6, and 12. And the multiples are 12, 24, and 36, etc… To avoid this confusion, always understand the concept separately.
Mistake 2
Ignoring the Negative Factors.
Always remember that each positive factor has consistent negative factors. For example, factors of 12 are ±1, ±2, ±3, ±4, ±6, ±12.
Mistake 3
Not checking Divisibility Properly
In some cases, children might wrongly 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 try to divide numbers systematically, and also pair them with larger factors.
Examples on Factors of 36
Problem 1
What is the GCF of 48 and 60?
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Common factors (48 and 60)are: 1, 2, 3, 4, 6, 12.
The GCF is 12.
Explanation
To find the Greatest Common Factor of both numbers 48 and 60, first list out the multiples of both numbers, then identify the common factors of both lists. After choosing, the greatest common factor (GCF) is 12.
Problem 2
onia has a mathematical doubt. Help her find the answer: is 48 divisible by 7?
48 ÷ 7 = 6.857 (Not a whole number)
Explanation
No, when calculating 48 divided by 7, to get the answer is 6.857. Which is not a whole number. So 7 is not a factor of 48.
Problem 3
Priya tries to find out the even factors of 48. How can we help her?
There are 8 even factors of 48.
The factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Even factors of 48: 2, 4, 6, 8, 12, 16, 24, and 48.
Explanation
The number 48 has Eight even factors. To find the even number, we write the whole factors and select the even numbers of the list.
Problem 4
A family in Los Angeles (LA) buys 48 snack packs from Costco for an NBA playoff watch party. They want to divide the snack packs into equal gift bags so that each guest gets the same number of snacks with none left over. What are all the possible numbers of gift bags they can make?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Explanation
To divide 48 snack packs evenly, the number of gift bags must divide 48 with no remainder.
Any number that divides 48 exactly is called a factor of 48.
By checking which numbers divide 48 evenly, we find all possible group sizes that work.
Problem 5
A Walgreens pharmacy in Chicago has 48 tablets of a medicine. 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 that can be placed in each pack?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Explanation
Each dosage pack must contain a number of tablets that divides 48 evenly.
These numbers are the factors of 48.
Since 48 can be divided without a remainder by these values, each one represents a valid dosage size.
Problem 6
A science class in Houston spends $48 on gas (priced per gallon) for a field trip. The teacher wants to split the total gas 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, 16, 24, 48
Explanation
To split $48 evenly, the number of students must divide 48 exactly.
These possible group sizes are the factors of 48.
Each factor represents a number of students who could share the cost equally without any remainder.
FAQs on Factors Of 48
1.Write down the odd factors of 48.
2.How do you find the GCF of 48 and another number?
3.Can a number have negative factors?
4.Can 48 fit as a perfect cube?
5.What are the perfect square factors of 48?
6.How many factors does 48 have?
7.What is the smallest factor of 48?
8.What is the largest factor of 48?
9.How many even factors does 48 have?
10.What are the odd factors of 48?
11.What is the sum of all the factors of 48?
Important Terms Related to Factors of 48
- Factors: Factors are numbers that divide a given number evenly, without leaving a 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 48 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.
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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.
