100 LearnersLast updated on May 26th, 2025
Factors of 336
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 336, how they are used in real life, and tips to learn them quickly.
What are the Factors of 336?
The numbers that divide 336 evenly are known as factors of 336.
A factor of 336 is a number that divides the number without remainder.
The factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, and 336.
Negative factors of 336: -1, -2, -3, -4, -6, -7, -8, -12, -14, -16, -21, -24, -28, -42, -48, -56, -84, -112, -168, and -336.
Prime factors of 336: 2, 3, and 7.
Prime factorization of 336: 2⁴ × 3 × 7.
The sum of factors of 336: 1 + 2 + 3 + 4 + 6 + 7 + 8 + 12 + 14 + 16 + 21 + 24 + 28 + 42 + 48 + 56 + 84 + 112 + 168 + 336 = 1,008
How to Find Factors of 336?
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 336. Identifying the numbers which are multiplied to get the number 336 is the multiplication method.
Step 1: Multiply 336 by 1, 336 × 1 = 336.
Step 2: Check for other numbers that give 336 after multiplying:
2 × 168 = 336
3 × 112 = 336
4 × 84 = 336
6 × 56 = 336
7 × 48 = 336
8 × 42 = 336
12 × 28 = 336
14 × 24 = 336
16 × 21 = 336
Therefore, the positive factor pairs of 336 are: (1, 336), (2, 168), (3, 112), (4, 84), (6, 56), (7, 48), (8, 42), (12, 28), (14, 24), and (16, 21). For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers 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 336 by 1, 336 ÷ 1 = 336.
Step 2: Continue dividing 336 by the numbers until the remainder becomes 0.
336 ÷ 1 = 336
336 ÷ 2 = 168
336 ÷ 3 = 112
336 ÷ 4 = 84
336 ÷ 6 = 56
336 ÷ 7 = 48
336 ÷ 8 = 42
336 ÷ 12 = 28
336 ÷ 14 = 24
336 ÷ 16 = 21
Therefore, the factors of 336 are: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, and 336.
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 336 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
336 ÷ 2 = 168
168 ÷ 2 = 84
84 ÷ 2 = 42
42 ÷ 2 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
The prime factors of 336 are 2, 3, and 7.
The prime factorization of 336 is: 2⁴ × 3 × 7.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 336 is divided by 2 to get 168.
Step 2: Now divide 168 by 2 to get 84.
Step 3: Then divide 84 by 2 to get 42.
Step 4: Divide 42 by 2 to get 21.
Step 5: Divide 21 by 3 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 336 is: 2⁴ × 3 × 7.
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 336: (1, 336), (2, 168), (3, 112), (4, 84), (6, 56), (7, 48), (8, 42), (12, 28), (14, 24), and (16, 21).
Negative factor pairs of 336: (-1, -336), (-2, -168), (-3, -112), (-4, -84), (-6, -56), (-7, -48), (-8, -42), (-12, -28), (-14, -24), and (-16, -21).
Common Mistakes and How to Avoid Them in Factors of 336
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and 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 336, 1 and 336 is also a factor.
Factors of 336 Examples
Problem 1
There are 12 teams in a tournament and 336 players. How will they divide the players equally?
They will have 28 players each.
Explanation
To divide the players equally, we need to divide the total players by the number of teams.
336/12 = 28
Problem 2
A garden is rectangular, the width of the garden is 14 meters and the total area is 336 square meters. Find the length?
24 meters.
Explanation
To find the length of the garden, we use the formula, Area = length × width
336 = 14 × length
To find the value of length, we need to shift 14 to the left side.
336/14 = length
Length = 24.
Problem 3
There are 24 baskets and 336 apples. How many apples will be in each basket?
Each basket will have 14 apples.
Explanation
To find the apples in each basket, divide the total apples by the number of baskets.
336/24 = 14
Problem 4
In a concert, there are 336 attendees, and 7 rows. How many attendees are there in each row?
There are 48 attendees in each row.
Explanation
Dividing the attendees by the total rows, we will get the number of attendees in each row.
336/7 = 48
Problem 5
336 books need to be arranged in 6 shelves. How many books will go on each shelf?
Each of the shelves has 56 books.
Explanation
Divide total books by shelves.
336/6 = 56
FAQs on Factors of 336
1.What are the factors of 336?
2.Mention the prime factors of 336.
3.Is 336 a multiple of 8?
4.Mention the factor pairs of 336?
5.What is the square of 336?
6.How can children in Canada use numbers in everyday life to understand Factors of 336?
7.What are some fun ways kids in Canada can practice Factors of 336 with numbers?
8.What role do numbers and Factors of 336 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 336 skills?
Important Glossaries for Factors of 336
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 336 are 1, 2, 3, 4, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 336.
- 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 336 are (1, 336), (2, 168), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For instance, 336 = 2⁴ × 3 × 7.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 336 is a multiple of 8.
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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.
