117 LearnersLast updated on May 26th, 2025
Factors of 1364
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 1364, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1364?
The numbers that divide 1364 evenly are known as factors of 1364.
A factor of 1364 is a number that divides the number without remainder.
The factors of 1364 are 1, 2, 4, 11, 22, 31, 44, 62, 124, 341, 682, and 1364.
Negative factors of 1364: -1, -2, -4, -11, -22, -31, -44, -62, -124, -341, -682, and -1364.
Prime factors of 1364: 2, 11, and 31.
Prime factorization of 1364: 2² × 11 × 31.
The sum of factors of 1364: 1 + 2 + 4 + 11 + 22 + 31 + 44 + 62 + 124 + 341 + 682 + 1364 = 2688
How to Find Factors of 1364?
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 1364. Identifying the numbers which are multiplied to get the number 1364 is the multiplication method.
Step 1: Multiply 1364 by 1, 1364 × 1 = 1364.
Step 2: Check for other numbers that give 1364 after multiplying
2 × 682 = 1364
4 × 341 = 1364
11 × 124 = 1364
22 × 62 = 1364
31 × 44 = 1364
Therefore, the positive factor pairs of 1364 are: (1, 1364), (2, 682), (4, 341), (11, 124), (22, 62), and (31, 44).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number 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 1364 by 1, 1364 ÷ 1 = 1364.
Step 2: Continue dividing 1364 by the numbers until the remainder becomes 0.
1364 ÷ 1 = 1364
1364 ÷ 2 = 682
1364 ÷ 4 = 341
1364 ÷ 11 = 124
1364 ÷ 22 = 62
1364 ÷ 31 = 44
Therefore, the factors of 1364 are: 1, 2, 4, 11, 22, 31, 44, 62, 124, 341, 682, 1364.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 1364 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
1364 ÷ 2 = 682
682 ÷ 2 = 341
341 ÷ 11 = 31
31 ÷ 31 = 1
The prime factors of 1364 are 2, 11, and 31.
The prime factorization of 1364 is: 2² × 11 × 31.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 1364 is divided by 2 to get 682.
Step 2: Now divide 682 by 2 to get 341.
Step 3: Then divide 341 by 11 to get 31. Here, 31 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1364 is: 2² × 11 × 31.
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 1364: (1, 1364), (2, 682), (4, 341), (11, 124), (22, 62), and (31, 44).
Negative factor pairs of 1364: (-1, -1364), (-2, -682), (-4, -341), (-11, -124), (-22, -62), and (-31, -44).
Common Mistakes and How to Avoid Them in Factors of 1364
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 1364, 1 and 1364 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 1364 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 1364/1.5 = 909.333, 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 1364 are prime numbers.
For example, 2, 11, and 31 are the prime factors of 1364, but it has other factors like 4, 22.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1364 as 2² × 11 × 31 and missing all the key factors.
Factors of 1364 Examples
Problem 1
There are 341 trees and 1364 apples. How will they distribute the apples equally?
They will get 4 apples each.
Explanation
To distribute the apples equally, we need to divide the total apples by the number of trees.
1364/341 = 4
Problem 2
A garden is rectangular, the length of the garden is 62 meters and the total area is 1364 square meters. Find the width?
22 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1364 = 62 × width
To find the value of width, we need to shift 62 to the left side.
1364/62 = width
Width = 22.
Problem 3
There are 44 boxes and 1364 marbles. How many marbles will be in each box?
Each box will have 31 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
1364/44 = 31
Problem 4
In a class, there are 1364 books, and 31 shelves. How many books are there on each shelf?
There are 44 books on each shelf.
Explanation
Dividing the books by the total shelves, we will get the number of books on each shelf.
1364/31 = 44
Problem 5
1364 chairs need to be arranged in 11 rows. How many chairs will be in each row?
Each row will have 124 chairs.
Explanation
Divide total chairs by the number of rows.
1364/11 = 124
FAQs on Factors of 1364
1.What are the factors of 1364?
2.Mention the prime factors of 1364.
3.Is 1364 a multiple of 22?
4.Mention the factor pairs of 1364?
5.What is the square of 1364?
Important Glossaries for Factor of 1364
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1364 are 1, 2, 4, 11, 22, 31, 44, 62, 124, 341, 682, and 1364.
- Prime factors: The factors which are prime numbers. For example, 2, 11, and 31 are prime factors of 1364.
- Prime factorization: Breaking down a number into its prime factors. For example, 1364 = 2² × 11 × 31.
- 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 1364 are (1, 1364), (2, 682), etc.
- Negative factors: Factors that are negative numbers. For example, the negative factors of 1364 are -1, -2, -4, etc.
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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.
