119 LearnersLast updated on May 26th, 2025
Factors of 1368
Factors are the numbers that divide any given number evenly without 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 1368, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1368?
The numbers that divide 1368 evenly are known as factors of 1368.
A factor of 1368 is a number that divides the number without remainder.
The factors of 1368 are 1, 2, 3, 4, 6, 8, 9, 12, 19, 24, 27, 36, 38, 57, 76, 114, 152, 171, 228, 342, 456, 684, and 1368.
Negative factors of 1368: -1, -2, -3, -4, -6, -8, -9, -12, -19, -24, -27, -36, -38, -57, -76, -114, -152, -171, -228, -342, -456, -684, and -1368.
Prime factors of 1368: 2, 3, and 19.
Prime factorization of 1368: 23 × 32 × 19.
The sum of factors of 1368: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 19 + 24 + 27 + 36 + 38 + 57 + 76 + 114 + 152 + 171 + 228 + 342 + 456 + 684 + 1368 = 4056
How to Find Factors of 1368?
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 1368. Identifying the numbers which are multiplied to get the number 1368 is the multiplication method.
Step 1: Multiply 1368 by 1, 1368 × 1 = 1368.
Step 2: Check for other numbers that give 1368 after multiplying
2 × 684 = 1368
3 × 456 = 1368
4 × 342 = 1368
6 × 228 = 1368
8 × 171 = 1368
9 × 152 = 1368
12 × 114 = 1368
19 × 72 = 1368
24 × 57 = 1368
27 × 76 = 1368
36 × 38 = 1368
Therefore, the positive factor pairs of 1368 are: (1, 1368), (2, 684), (3, 456), (4, 342), (6, 228), (8, 171), (9, 152), (12, 114), (19, 72), (24, 57), (27, 76), (36, 38).
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 1368 by 1, 1368 ÷ 1 = 1368.
Step 2: Continue dividing 1368 by the numbers until the remainder becomes 0.
1368 ÷ 1 = 1368
1368 ÷ 2 = 684
1368 ÷ 3 = 456
1368 ÷ 4 = 342
1368 ÷ 6 = 228
1368 ÷ 8 = 171
1368 ÷ 9 = 152
1368 ÷ 12 = 114
1368 ÷ 19 = 72
1368 ÷ 24 = 57
1368 ÷ 27 = 76
1368 ÷ 36 = 38
Therefore, the factors of 1368 are: 1, 2, 3, 4, 6, 8, 9, 12, 19, 24, 27, 36, 38, 57, 76, 114, 152, 171, 228, 342, 456, 684, 1368.
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 1368 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
1368 ÷ 2 = 684
684 ÷ 2 = 342
342 ÷ 2 = 171
171 ÷ 3 = 57
57 ÷ 3 = 19 19 ÷ 19 = 1
The prime factors of 1368 are 2, 3, and 19.
The prime factorization of 1368 is: 2^3 × 3^2 × 19.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1368 is divided by 2 to get 684.
Step 2: Now divide 684 by 2 to get 342.
Step 3: Then divide 342 by 2 to get 171.
Step 4: Divide 171 by 3 to get 57. Step 5: Divide 57 by 3 to get 19. Here, 19 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1368 is: 23 × 32 × 19.
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 1368: (1, 1368), (2, 684), (3, 456), (4, 342), (6, 228), (8, 171), (9, 152), (12, 114), (19, 72), (24, 57), (27, 76), (36, 38).
Negative factor pairs of 1368: (-1, -1368), (-2, -684), (-3, -456), (-4, -342), (-6, -228), (-8, -171), (-9, -152), (-12, -114), (-19, -72), (-24, -57), (-27, -76), (-36, -38).
Common Mistakes and How to Avoid Them in Factors of 1368
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1368, 1 and 1368 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 1368 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 1368/1.5 = 912, 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 1368 are prime numbers.
For example, 2, 3, and 19 are the prime factors of 1368, but it has other factors like 4, 6, 38.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1368 as 23 × 32 × 19 and missing all the key factors.
Factors of 1368 Examples
Problem 1
There are 12 teams and 1368 participants. How will they be divided equally among the teams?
Each team will have 114 participants.
Explanation
To divide the participants equally, we need to divide the total participants with the number of teams.
1368/12 = 114
Problem 2
A garden is rectangular, the length of the garden is 38 meters and the total area is 1368 square meters. Find the width.
36 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1368 = 38 × width
To find the value of width, we need to shift 38 to the left side.
1368/38 = width
Width = 36.
Problem 3
There are 19 boxes and 1368 apples. How many apples will be in each box?
Each box will have 72 apples.
Explanation
To find the apples in each box, divide the total apples with the boxes.
1368/19 = 72
Problem 4
In a class, there are 342 students, and 6 groups. How many students are there in each group?
There are 57 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
342/6 = 57
Problem 5
1368 books need to be arranged in 24 shelves. How many books will go on each shelf?
Each of the shelves has 57 books.
Explanation
Divide total books with shelves.
1368/24 = 57
FAQs on Factors of 1368
1.What are the factors of 1368?
2.Mention the prime factors of 1368.
3.Is 1368 a multiple of 9?
4.Mention the factor pairs of 1368?
5.What is the square of 1368?
Important Glossaries for Factors of 1368
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1368 are 1, 2, 3, 4, 6, 8, 9, 12, 19, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 19 are prime factors of 1368.
- 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 1368 are (1, 1368), (2, 684), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1368 is 23 × 32 × 19.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 1368 is a multiple of 9.
Explore More numbers
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.
