102 LearnersLast updated on May 26th, 2025
Factors of 308
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 308, how they are used in real life, and tips to learn them quickly.
What are the Factors of 308?
The numbers that divide 308 evenly are known as factors of 308.
A factor of 308 is a number that divides the number without remainder.
The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, and 308.
Negative factors of 308: -1, -2, -4, -7, -11, -14, -22, -28, -44, -77, -154, and -308.
Prime factors of 308: 2, 7, and 11.
Prime factorization of 308: 2² × 7 × 11.
The sum of factors of 308: 1 + 2 + 4 + 7 + 11 + 14 + 22 + 28 + 44 + 77 + 154 + 308 = 672
How to Find Factors of 308?
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 308. Identifying the numbers which are multiplied to get the number 308 is the multiplication method.
Step 1: Multiply 308 by 1, 308 × 1 = 308.
Step 2: Check for other numbers that give 308 after multiplying
2 × 154 = 308
4 × 77 = 308
7 × 44 = 308
11 × 28 = 308
14 × 22 = 308
Therefore, the positive factor pairs of 308 are: (1, 308), (2, 154), (4, 77), (7, 44), (11, 28), (14, 22).
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 308 by 1, 308 ÷ 1 = 308.
Step 2: Continue dividing 308 by the numbers until the remainder becomes 0.
308 ÷ 1 = 308
308 ÷ 2 = 154
308 ÷ 4 = 77
308 ÷ 7 = 44
308 ÷ 11 = 28
308 ÷ 14 = 22
Therefore, the factors of 308 are: 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308.
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 308 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
308 ÷ 2 = 154
154 ÷ 2 = 77
77 ÷ 7 = 11
11 ÷ 11 = 1
The prime factors of 308 are 2, 7, and 11.
The prime factorization of 308 is: 2² × 7 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 308 is divided by 2 to get 154.
Step 2: Now divide 154 by 2 to get 77.
Step 3: Then divide 77 by 7 to get 11. Here, 11 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 308 is: 2² × 7 × 11.
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 308: (1, 308), (2, 154), (4, 77), (7, 44), (11, 28), and (14, 22).
Negative factor pairs of 308: (-1, -308), (-2, -154), (-4, -77), (-7, -44), (-11, -28), and (-14, -22).
Common Mistakes and How to Avoid Them in Factors of 308
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 308, 1 and 308 are also factors.
Factors of 308 Examples
Problem 1
There are 14 students and 308 pencils. How will they distribute them equally?
They will get 22 pencils each.
Explanation
To distribute the pencils equally, we need to divide the total pencils by the number of students.
308/14 = 22
Problem 2
A garden is rectangular, the length of the garden is 11 meters and the total area is 308 square meters. Find the width?
28 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
308 = 11 × width
To find the value of width, we need to shift 11 to the left side.
308/11 = width
Width = 28.
Problem 3
There are 44 boxes, and 308 marbles. How many marbles will be in each box?
Each box will have 7 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
308/44 = 7
Problem 4
In a theater, there are 308 seats, and 11 rows. How many seats are there in each row?
There are 28 seats in each row.
Explanation
Dividing the seats by the total rows, we will get the number of seats in each row.
308/11 = 28
Problem 5
308 books need to be arranged in 14 shelves. How many books will go on each shelf?
Each of the shelves has 22 books.
Explanation
Divide total books by shelves.
308/14 = 22
FAQs on Factors of 308
1.What are the factors of 308?
2.Mention the prime factors of 308.
3.Is 308 a multiple of 11?
4.Mention the factor pairs of 308?
5.What is the square of 308?
6.How can children in Canada use numbers in everyday life to understand Factors of 308?
7.What are some fun ways kids in Canada can practice Factors of 308 with numbers?
8.What role do numbers and Factors of 308 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 308 skills?
Important Glossaries for Factors of 308
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, and 308.
- Prime factors: The factors which are prime numbers. For example, 2, 7, and 11 are prime factors of 308.
- 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 308 are (1, 308), (2, 154), etc.
- Prime factorization: It is expressing a number as the product of its prime factors. For example, 308 = 2² × 7 × 11.
- Multiplication method: A technique to find factors by identifying pairs of numbers that multiply to give the original number, like identifying (11, 28) for 308.
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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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