101 LearnersLast updated on May 26th, 2025
Factors of 312
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 312, how they are used in real life, and tips to learn them quickly.
What are the Factors of 312?
The numbers that divide 312 evenly are known as factors of 312. A factor of 312 is a number that divides the number without remainder.
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, and 312.
Negative factors of 312: -1, -2, -3, -4, -6, -8, -12, -13, -24, -26, -39, -52, -78, -104, -156, and -312.
Prime factors of 312: 2 and 3, 13.
Prime factorization of 312: 2³ × 3 × 13.
The sum of factors of 312: 1 + 2 + 3 + 4 + 6 + 8 + 12 + 13 + 24 + 26 + 39 + 52 + 78 + 104 + 156 + 312 = 840.
How to Find Factors of 312?
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 312. Identifying the numbers which are multiplied to get the number 312 is the multiplication method.
Step 1: Multiply 312 by 1, 312 × 1 = 312.
Step 2: Check for other numbers that give 312 after multiplying
2 × 156 = 312
3 × 104 = 312
4 × 78 = 312
6 × 52 = 312
8 × 39 = 312
12 × 26 = 312
13 × 24 = 312
Therefore, the positive factor pairs of 312 are: (1, 312), (2, 156), (3, 104), (4, 78), (6, 52), (8, 39), (12, 26), (13, 24).
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 312 by 1, 312 ÷ 1 = 312.
Step 2: Continue dividing 312 by the numbers until the remainder becomes 0.
312 ÷ 1 = 312
312 ÷ 2 = 156
312 ÷ 3 = 104
312 ÷ 4 = 78
312 ÷ 6 = 52
312 ÷ 8 = 39
312 ÷ 12 = 26
312 ÷ 13 = 24
Therefore, the factors of 312 are: 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 312 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
312 ÷ 2 = 156
156 ÷ 2 = 78
78 ÷ 2 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1
The prime factors of 312 are 2, 3, and 13.
The prime factorization of 312 is: 2³ × 3 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 312 is divided by 2 to get 156.
Step 2: Now divide 156 by 2 to get 78.
Step 3: Then divide 78 by 2 to get 39.
Step 4: Divide 39 by 3 to get 13. Here, 13 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 312 is: 2³ × 3 × 13.
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 312: (1, 312), (2, 156), (3, 104), (4, 78), (6, 52), (8, 39), (12, 26), (13, 24).
Negative factor pairs of 312: (-1, -312), (-2, -156), (-3, -104), (-4, -78), (-6, -52), (-8, -39), (-12, -26), (-13, -24).
Common Mistakes and How to Avoid Them in Factors of 312
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 312, 1 and 312 is also a factor.
Factors of 312 Examples
Problem 1
There are 6 teams and 312 participants. How will they divide the participants equally?
They will have 52 participants each.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
312/6 = 52
Problem 2
A garden is rectangular, the length of the garden is 12 meters and the total area is 312 square meters. Find the width?
26 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
312 = 12 × width
To find the value of width, we need to shift 12 to the left side.
312/12 = width
Width = 26.
Problem 3
There are 13 boxes and 312 apples. How many apples will be in each box?
Each box will have 24 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
312/13 = 24
Problem 4
In a class, there are 312 students, and 8 groups. How many students are there in each group?
There are 39 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
312/8 = 39
Problem 5
312 books need to be arranged in 12 shelves. How many books will go on each shelf?
Each of the shelves has 26 books.
Explanation
Divide total books by shelves.
312/12 = 26
FAQs on Factors of 312
1.What are the factors of 312?
2.Mention the prime factors of 312.
3.Is 312 a multiple of 4?
4.Mention the factor pairs of 312?
5.What is the square of 312?
6.How can children in Canada use numbers in everyday life to understand Factors of 312?
7.What are some fun ways kids in Canada can practice Factors of 312 with numbers?
8.What role do numbers and Factors of 312 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 312 skills?
Important Glossaries for Factor of 312
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, and 312.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 13 are prime factors of 312.
- 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 312 are (1, 312), (2, 156), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 312 is 2³ × 3 × 13.
- Multiples: A multiple of a number is the product of that number and an integer. For example, 312 is a multiple of 4.
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About BrightChamps in Canada
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.
