119 LearnersLast updated on May 26th, 2025
Factors of 1344
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 1344, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1344?
The numbers that divide 1344 evenly are known as factors of 1344.
A factor of 1344 is a number that divides the number without remainder.
The factors of 1344 include 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 192, 224, 336, 448, 672, and 1344.
Negative factors of 1344: -1, -2, -3, -4, -6, -7, -8, -12, -14, -16, -21, -24, -28, -32, -42, -48, -56, -84, -96, -112, -168, -192, -224, -336, -448, -672, and -1344.
Prime factors of 1344: 2 and 3, and 7.
Prime factorization of 1344: 26 × 3 × 7.
The sum of factors of 1344: 1 + 2 + 3 + 4 + 6 + 7 + 8 + 12 + 14 + 16 + 21 + 24 + 28 + 32 + 42 + 48 + 56 + 84 + 96 + 112 + 168 + 192 + 224 + 336 + 448 + 672 + 1344 = 4032
How to Find Factors of 1344?
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 1344. Identifying the numbers which are multiplied to get the number 1344 is the multiplication method.
Step 1: Multiply 1344 by 1, 1344 × 1 = 1344.
Step 2: Check for other numbers that give 1344 after multiplying
2 × 672 = 1344
3 × 448 = 1344
4 × 336 = 1344
6 × 224 = 1344
7 × 192 = 1344
8 × 168 = 1344
12 × 112 = 1344
14 × 96 = 1344
16 × 84 = 1344
21 × 64 = 1344
24 × 56 = 1344
28 × 48 = 1344
32 × 42 = 1344
Therefore, the positive factor pairs of 1344 are: (1, 1344), (2, 672), (3, 448), (4, 336), (6, 224), (7, 192), (8, 168), (12, 112), (14, 96), (16, 84), (21, 64), (24, 56), (28, 48), (32, 42).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the 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 1344 by 1, 1344 ÷ 1 = 1344.
Step 2: Continue dividing 1344 by the numbers until the remainder becomes 0.
1344 ÷ 1 = 1344
1344 ÷ 2 = 672
1344 ÷ 3 = 448
1344 ÷ 4 = 336
1344 ÷ 6 = 224
1344 ÷ 7 = 192
1344 ÷ 8 = 168
1344 ÷ 12 = 112
1344 ÷ 14 = 96
1344 ÷ 16 = 84
1344 ÷ 21 = 64
1344 ÷ 24 = 56
1344 ÷ 28 = 48
1344 ÷ 32 = 42
Therefore, the factors of 1344 are: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 192, 224, 336, 448, 672, 1344.
Prime Factors and Prime Factorization
The factors can be found by dividing it 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 1344 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1344 ÷ 2 = 672
672 ÷ 2 = 336
336 ÷ 2 = 168
168 ÷ 2 = 84
84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
The prime factors of 1344 are 2, 3, and 7.
The prime factorization of 1344 is: 2^6 × 3 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1344 is divided by 2 to get 672.
Step 2: Now divide 672 by 2 to get 336.
Step 3: Then divide 336 by 2 to get 168.
Step 4: Divide 168 by 2 to get 84.
Step 5: Divide 84 by 2 to get 42.
Step 6: Divide 42 by 2 to get 21.
Step 7: Divide 21 by 3 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1344 is: 26 × 3 × 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 1344: (1, 1344), (2, 672), (3, 448), (4, 336), (6, 224), (7, 192), (8, 168), (12, 112), (14, 96), (16, 84), (21, 64), (24, 56), (28, 48), (32, 42).
Negative factor pairs of 1344: (-1, -1344), (-2, -672), (-3, -448), (-4, -336), (-6, -224), (-7, -192), (-8, -168), (-12, -112), (-14, -96), (-16, -84), (-21, -64), (-24, -56), (-28, -48), (-32, -42).
Common Mistakes and How to Avoid Them in Factors of 1344
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 1344, 1 and 1344 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1344 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1344/1.5 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 1344 are prime numbers.
For example, 2, 3, and 7 are the prime factors of 1344, but it has other factors like 4, 6, 12, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1344 as 26 × 3 × 7 and missing all the key factors.
Factors of 1344 Examples
Problem 1
A school has 1344 chairs to arrange in rows. Each row should have 28 chairs. How many rows will be formed?
48 rows.
Explanation
To find the number of rows, divide the total chairs by the chairs per row.
1344/28 = 48
Problem 2
A garden is rectangular, the length of the garden is 112 meters and the total area is 1344 square meters. Find the width.
12 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1344 = 112 × width
To find the value of width, we need to shift 112 to the left side.
1344/112 = width
Width = 12.
Problem 3
There are 168 boxes and 1344 apples. How many apples will be in each box?
Each box will have 8 apples.
Explanation
To find the apples in each box, divide the total apples by the number of boxes.
1344/168 = 8
Problem 4
In a hall, there are 1344 seats and 96 groups. How many seats are there in each group?
There are 14 seats in each group.
Explanation
Dividing the seats by the total groups, we will get the number of seats in each group.
1344/96 = 14
Problem 5
1344 books need to be arranged in 56 shelves. How many books will go on each shelf?
Each of the shelves has 24 books.
Explanation
Divide total books by shelves.
1344/56 = 24
FAQs on Factors of 1344
1.What are the factors of 1344?
2.Mention the prime factors of 1344.
3.Is 1344 a multiple of 7?
4.Mention the factor pairs of 1344.
5.What is the square of 1344?
6.How can children in Australia use numbers in everyday life to understand Factors of 1344?
7.What are some fun ways kids in Australia can practice Factors of 1344 with numbers?
8.What role do numbers and Factors of 1344 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 1344 skills?
Important Glossaries for Factor of 1344
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1344 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 192, 224, 336, 448, 672, and 1344.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 1344.
- 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 1344 are (1, 1344), (2, 672), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 1344 is 26 × 3 × 7.
- Multiplication method: A way to find factors by identifying pairs of numbers that multiply to the original number, such as finding factor pairs of 1344 through multiplication.
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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
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