125 LearnersLast updated on May 26th, 2025
Factors of 224
Factors are the numbers that divide any given number evenly without a 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 224, how they are used in real life, and tips to learn them quickly.
What are the Factors of 224?
The numbers that divide 224 evenly are known as factors of 224.
A factor of 224 is a number that divides the number without a remainder.
The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, and 224.
Negative factors of 224: -1, -2, -4, -7, -8, -14, -16, -28, -32, -56, -112, and -224.
Prime factors of 224: 2 and 7.
Prime factorization of 224: 25 × 7.
The sum of factors of 224: 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 32 + 56 + 112 + 224 = 504
How to Find Factors of 224?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using 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 224. Identifying the numbers which are multiplied to get the number 224 is the multiplication method.
Step 1: Multiply 224 by 1, 224 × 1 = 224.
Step 2: Check for other numbers that give 224 after multiplying
2 × 112 = 224
4 × 56 = 224
7 × 32 = 224
8 × 28 = 224
14 × 16 = 224
Therefore, the positive factor pairs of 224 are: (1, 224), (2, 112), (4, 56), (7, 32), (8, 28), (14, 16).
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 224 by 1, 224 ÷ 1 = 224.
Step 2: Continue dividing 224 by the numbers until the remainder becomes 0.
224 ÷ 1 = 224
224 ÷ 2 = 112
224 ÷ 4 = 56
224 ÷ 7 = 32
224 ÷ 8 = 28
224 ÷ 14 = 16
Therefore, the factors of 224 are: 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224.
Prime Factors and Prime Factorization
The factors can be found by dividing 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 224 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
224 ÷ 2 = 112
112 ÷ 2 = 56
56 ÷ 2 = 28
28 ÷ 2 = 14
14 ÷ 2 = 7
7 ÷ 7 = 1
The prime factors of 224 are 2 and 7.
The prime factorization of 224 is: 2^5 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 224 is divided by 2 to get 112.
Step 2: Now divide 112 by 2 to get 56.
Step 3: Then divide 56 by 2 to get 28.
Step 4: Divide 28 by 2 to get 14.
Step 5: Divide 14 by 2 to get 7.
Here, 7 is a prime number that cannot be divided anymore.
So, the prime factorization of 224 is: 25 × 7.
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 224: (1, 224), (2, 112), (4, 56), (7, 32), (8, 28), and (14, 16).
Negative factor pairs of 224: (-1, -224), (-2, -112), (-4, -56), (-7, -32), (-8, -28), and (-14, -16).
Common Mistakes and How to Avoid Them in Factors of 224
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 number. Always remember to include 1 and the number itself.
For example, in factors of 224, 1 and 224 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 224 include -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because 224/1.5 = 149.333, 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 224 are prime numbers. For example, 2 and 7 are the prime factors of 224, but it has other factors like 4, 28.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 224 as 2^5 × 7 and missing key factors.
Factors of 224 Examples
Problem 1
A farmer has 224 apples and 8 baskets. How many apples will each basket contain if he distributes them equally?
Each basket will contain 28 apples.
Explanation
To divide the apples equally, we need to divide the total apples by the number of baskets.
224/8 = 28
Problem 2
A rectangular garden has an area of 224 square meters and a width of 14 meters. What is the length of the garden?
16 meters.
Explanation
To find the length of the garden, use the formula,
Area = length × width
224 = length × 14
To find the value of length, divide 224 by 14.
224/14 = length
Length = 16.
Problem 3
A warehouse has 32 boxes, each containing an equal number of items, with a total of 224 items. How many items are in each box?
Each box contains 7 items.
Explanation
To find the number of items per box, divide the total items by the number of boxes.
224/32 = 7
Problem 4
In a workshop, 224 pieces of wood need to be divided into 56 equal sets. How many pieces will be in each set?
Each set will have 4 pieces.
Explanation
Divide the total pieces by the number of sets to get pieces in each set.
224/56 = 4
Problem 5
A school has 224 students and 14 classrooms. How many students will be in each classroom if they are evenly distributed?
Each classroom will have 16 students.
Explanation
Dividing the students by the number of classrooms gives the number of students per classroom.
224/14 = 16
FAQs on Factors of 224
1.What are the factors of 224?
2.Mention the prime factors of 224.
3.Is 224 a multiple of 8?
4.Mention the factor pairs of 224.
5.What is the square of 224?
6.How can children in United Arab Emirates use numbers in everyday life to understand Factors of 224?
7.What are some fun ways kids in United Arab Emirates can practice Factors of 224 with numbers?
8.What role do numbers and Factors of 224 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve Factors of 224 skills?
Important Glossaries for Factors of 224
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, and 224.
- Prime factors: The factors that are prime numbers. For example, 2 and 7 are prime factors of 224.
- 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 224 are (1, 224), (2, 112), etc.
- Prime factorization: Breaking down a number into its smallest prime factors. For example, the prime factorization of 224 is 2^5 × 7.
- Multiple: A number that can be divided by another number without a remainder. For example, 224 is a multiple of 8.
Explore More numbers
![Important Math Links Icon]()
Previous to Factors of 224
About BrightChamps in United Arab Emirates
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.
