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481 LearnersLast updated on December 17, 2025
Factors of 56
A number that divides another number exactly without leaving any remainder is called a factor of the given number. Factors play an important role in mathematics and real-life situations, such as deciding the best time to schedule work shifts and events.
What are the Factors of 56?
Factors almost often come in pairs. There are several methods to find factors, which we will learn in the following sections. The factors of 56 are:1, 2, 4, 7, 8, 14, 28, and 56
The factors of 56 can be written as shown in the table given below:
| Factor Type | Values |
| Positive Factors of 56 | 1, 2, 4, 7, 8, 14, 28, 56 |
| Negative Factors of 56 | −1, −2, −4, −7, −8, −14, −28, −56 |
| Prime Factors of 56 | 2, 7 |
| Prime Factorization of 56 | 2 × 2 × 2 × 7 = 2³ × 7 |
| The sum of the Factors of 56 | 120 |
How To Find The Factors of 56
To find factors, kids use different methods for easier calculation. A few commonly used methods are as follows:
- Use of Multiplication Method
- Use of Division Method
- Use of Prime Factors and Prime Factorization
So, here we discuss a detailed explanation of the following methods:
Finding Factors Using Multiplication Method
In the multiplication method, we will try to find out the numbers that multiply together to give the value, 56. We will check the factors step by step:
Step 1: Start to multiply with numbers, which gives the value of 56.
Start with 1, and continue to multiply with other numbers.
1 × 56 = 56
2 × 28 = 56
4 × 14 = 56
7 × 8 = 56
Step 2: After the calculation, we get to these numbers, the factors of 56.
Step 3: The positive factor pairs of 56 found through multiplication are (1,56), (2,8), (4,14), (7,8)
Step 4: The negative factor pairs of 56 are (-1,-56), (-2,-8), (-4,-14), (-7,-8)
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Finding Factors Using Division Method
Using this method we will break down the given number till our remainder is zero. Let us go through the step-by-step process to find the factors of 56:
Step 1: Divide 56 by smaller numbers and see if there is any remainder. E.g., 56/1 = 56.
Step 2: We will continue in the same way and check for other numbers as well. For 56, the factors are 1, 2, 4, 7, 8, 14, 28, and 56. Because 56 can be divided evenly by these numbers.
Prime Factors and Prime Factorization
In the prime factorization method, we break down a number into its prime factor. The prime factors of 56 are 2 and 7. The prime factors can be found using the methods given below:
2 is the smallest prime number, so start dividing with two. And then continue to divide with other prime numbers.
56 ÷ 2 = 28
28 ÷ 2 = 14
14 ÷ 2 = 7
7 ÷ 7 = 1
The prime factorization of 56 is :
56= 2 3× 71
With prime factorization, 56 can be broken down into prime factors, 2 and 7.
Prime Factors of 56
Prime Factorization of 56
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: 56 divided by 2 gives us the quotient 28.
Step 2: Since 28 is not a prime number, it can be divided further.
56 ÷ 2 = 28
28 ÷ 2 = 14
14 ÷ 2 = 7
7 ÷ 7 = 1
The prime factorization of 56 is written below :
56 = 23 × 71.
Factor Pairs of 56
The factors of 56 can be written in both positive and negative pairs. The table below represents the factor pairs of 56, where the product of each pair of numbers is equal to 56.
Positive Pair Factors of 56:
| Factors | Positive Pair Factors |
| 1 × 56 = 56 | 1, 56 |
| 2 × 28 = 56 | 2, 28 |
| 4 × 14 = 56 | 4, 14 |
| 7 × 8 = 56 | 7, 8 |
Since the product of two negative numbers is also positive, 56 also has negative pair factors.
Negative Pair Factors of 56:
| Factors | Negative Pair Factors |
| −1 × −56 = 56 | −1, −56 |
| −2 × −28 = 56 | −2, −28 |
| −4 × −14 = 56 | −4, −14 |
| −7 × −8 = 56 | −7, −8 |
Common Mistakes and How to Avoid Them in Factors Of 56
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, etc… To avoid this confusion, always understand the concept separately.
Mistake 2
Ignoring the Negative Factors.
Always remember that each positive factor has a consistent 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 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 56
Problem 1
If a ribbon is 56 cm long, can it be cut into equal pieces of 28 cm?
Yes, 2 pieces.
Explanation
Dividing 56 by 28, we get 2, with no remainder. Which means 28 is the factor of 56.
Problem 2
What is the GCF of 56 and 72?
The GCF of 56 and 72 is 8.
Explanation
The GCF of 56 and 72 is the largest number that divides both 56 and 72 evenly.
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Common factors of both list: 8
GCF is 8.
Problem 3
A box contains 56 chocolates. How to divide them among 28 children equally?
Yes, everyone gets 2 chocolates.
Explanation
Yes, 56 chocolates can be shared equally among 28 children. Each child will get 2 chocolates, with nothing left over.
Problem 4
At a Costco warehouse in Chicago, a store manager receives 56 snack packs to distribute equally among pop-up kiosks in Dallas. Each kiosk must receive the same number of packs with none left over. What are all the possible numbers of kiosks that can be used for this distribution?
1, 2, 4, 7, 8, 14, 28, 56
Explanation
This problem asks for all numbers that divide 56 evenly with no remainder.
These numbers are the factors of 56. By listing all divisor pairs of 56 (1×56, 2×28, 4×14, 7×8), we find all possible kiosk counts.
Problem 5
A pharmacist at CVS in New York City has 56 mg of liquid medicine that must be divided equally into identical doses for patients in Boston. Each dose must be a whole number of milligrams. What are the possible dose sizes (in mg) that can be prepared?
1 mg, 2 mg, 4 mg, 7 mg, 8 mg, 14 mg, 28 mg, 56 mg
Explanation
The dose sizes must divide 56 mg evenly.
Therefore, we list all the factors of 56, which represent every possible whole-number dosage that can be made without leftovers.
Problem 6
An NFL youth training camp in Houston organizes 56 players for a road trip to Seattle. Coaches want to split the players into equal-sized practice groups. At the same time, the team bus refuels 56 gallons of gas, measured at $4 per gallon, with the cost shared evenly among the groups. What group sizes allow both the players and gas cost to be divided evenly?
1, 2, 4, 7, 8, 14, 28, 56
Explanation
For both the players and fuel cost to split evenly, the group size must divide 56 exactly.
These valid group sizes are the factors of 56, found by identifying all numbers that multiply in pairs to give 56.
FAQs on Factors of 56
1.Is 56 a perfect cube?
2.Does prime factorization follow rules?
3.Product of prime factors of 56
4.Can 56 be divided evenly by 7?
5.What is the LCM of 56 and 28?
6.How many factors does 56 have?
7.What is the smallest factor of 56?
8.What is the largest factor of 56?
9.Which factors of 56 add up to 13?
10.How many even factors does 56 have?
11.What are the odd factors of 56?
12.What is the sum of all the factors of 56?
Important Terms Related to Factors of 56
- 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 56, the prime factors are 2 and 7.
- 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).
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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.
