137 LearnersLast updated on May 28th, 2025
Factors of 1312
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 1312, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1312?
The numbers that divide 1312 evenly are known as factors of 1312.
A factor of 1312 is a number that divides the number without a remainder.
The factors of 1312 are 1, 2, 4, 8, 16, 32, 41, 82, 164, 328, 656, and 1312.
Negative factors of 1312: -1, -2, -4, -8, -16, -32, -41, -82, -164, -328, -656, and -1312.
Prime factors of 1312: 2 and 41.
Prime factorization of 1312: 25 × 41.
The sum of factors of 1312: 1 + 2 + 4 + 8 + 16 + 32 + 41 + 82 + 164 + 328 + 656 + 1312 = 2646
How to Find Factors of 1312?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 1312. Identifying the numbers which are multiplied to get the number 1312 is the multiplication method.
Step 1: Multiply 1312 by 1, 1312 × 1 = 1312.
Step 2: Check for other numbers that give 1312 after multiplying
2 × 656 = 1312
4 × 328 = 1312
8 × 164 = 1312
16 × 82 = 1312
32 × 41 = 1312
Therefore, the positive factor pairs of 1312 are: (1, 1312), (2, 656), (4, 328), (8, 164), (16, 82), (32, 41).
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 in whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 1312 by 1, 1312 ÷ 1 = 1312.
Step 2: Continue dividing 1312 by the numbers until the remainder becomes 0.
1312 ÷ 1 = 1312
1312 ÷ 2 = 656
1312 ÷ 4 = 328
1312 ÷ 8 = 164
1312 ÷ 16 = 82
1312 ÷ 32 = 41
Therefore, the factors of 1312 are: 1, 2, 4, 8, 16, 32, 41, 82, 164, 328, 656, 1312.
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 1312 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1312 ÷ 2 = 656
656 ÷ 2 = 328
328 ÷ 2 = 164
164 ÷ 2 = 82
82 ÷ 2 = 41
41 ÷ 41 = 1
The prime factors of 1312 are 2 and 41.
The prime factorization of 1312 is: 25 × 41.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1312 is divided by 2 to get 656.
Step 2: Now divide 656 by 2 to get 328.
Step 3: Then divide 328 by 2 to get 164.
Step 4: Divide 164 by 2 to get 82.
Step 5: Divide 82 by 2 to get 41.
Here, 41 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 1312 is: 25 × 41.
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 1312: (1, 1312), (2, 656), (4, 328), (8, 164), (16, 82), (32, 41).
Negative factor pairs of 1312: (-1, -1312), (-2, -656), (-4, -328), (-8, -164), (-16, -82), (-32, -41).
Common Mistakes and How to Avoid Them in Factors of 1312
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 word. Always remember to include 1 and the number itself.
For example, in factors of 1312, 1 and 1312 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 1312 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1312/1.5 = 874.666, 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 1312 are prime numbers.
For example, 2 and 41 are the prime factors of 1312, but it has other factors like 4, 8, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1312 as 25 × 41 and missing all the key factors.
Factors of 1312 Examples
Problem 1
There are 16 students and 1312 pages of a book. How many pages will each student get if divided equally?
Each student will get 82 pages.
Explanation
To divide the pages equally, we need to divide the total pages by the number of students.
1312/16 = 82
Problem 2
A hall is rectangular, the length of the hall is 41 meters and the total area is 1312 square meters. Find the width.
32 meters.
Explanation
To find the width of the hall, we use the formula,
Area = length × width
1312 = 41 × width
To find the value of width, we need to shift 41 to the left side.
1312/41 = width
Width = 32.
Problem 3
There are 164 boxes and 1312 candies. How many candies will be in each box?
Each box will have 8 candies.
Explanation
To find the candies in each box, divide the total candies by the boxes.
1312/164 = 8
Problem 4
In a workshop, there are 82 machines and a total of 1312 tasks. How many tasks are assigned to each machine?
There are 16 tasks assigned to each machine.
Explanation
Dividing the tasks by the total machines, we will get the number of tasks for each machine.
1312/82 = 16
Problem 5
1312 chairs need to be arranged in 41 rows. How many chairs will go in each row?
Each of the rows has 32 chairs.
Explanation
Divide the total chairs by the rows.
1312/41 = 32
FAQs on Factors of 1312
1.What are the factors of 1312?
2.Mention the prime factors of 1312.
3.Is 1312 a multiple of 8?
4.Mention the factor pairs of 1312?
5.What is the square of 1312?
6.How can children in United States use numbers in everyday life to understand Factors of 1312?
7.What are some fun ways kids in United States can practice Factors of 1312 with numbers?
8.What role do numbers and Factors of 1312 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 1312 skills?
Important Glossaries for Factors of 1312
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1312 are 1, 2, 4, 8, 16, 32, 41, 82, 164, 328, 656, and 1312.
- Prime factors: The factors which are prime numbers. For example, 2 and 41 are prime factors of 1312.
- 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 1312 are (1, 1312), (2, 656), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 1312 is 25 × 41.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, finding factor pairs of 1312 using multiplication, such as (32, 41).
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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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