102 LearnersLast updated on May 26th, 2025
Factors of 378
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 378, how they are used in real life, and tips to learn them quickly.
What are the Factors of 378?
The numbers that divide 378 evenly are known as factors of 378. A factor of 378 is a number that divides the number without remainder.
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, and 378.
Negative factors of 378: -1, -2, -3, -6, -7, -9, -14, -18, -21, -27, -42, -54, -63, -126, -189, and -378.
Prime factors of 378: 2, 3, and 7.
Prime factorization of 378: 2 × 33 × 7.
The sum of factors of 378: 1 + 2 + 3 + 6 + 7 + 9 + 14 + 18 + 21 + 27 + 42 + 54 + 63 + 126 + 189 + 378 = 1008
How to Find Factors of 378?
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 378. Identifying the numbers which are multiplied to get the number 378 is the multiplication method.
Step 1: Multiply 378 by 1, 378 × 1 = 378.
Step 2: Check for other numbers that give 378 after multiplying
2 × 189 = 378
3 × 126 = 378
6 × 63 = 378
7 × 54 = 378
9 × 42 = 378
18 × 21 = 378
Therefore, the positive factor pairs of 378 are: (1, 378), (2, 189), (3, 126), (6, 63), (7, 54), (9, 42), and (18, 21). 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 378 by 1, 378 ÷ 1 = 378.
Step 2: Continue dividing 378 by the numbers until the remainder becomes 0.
378 ÷ 1 = 378
378 ÷ 2 = 189
378 ÷ 3 = 126
378 ÷ 6 = 63
378 ÷ 7 = 54
378 ÷ 9 = 42
378 ÷ 18 = 21
Therefore, the factors of 378 are: 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378.
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 378 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
378 ÷ 2 = 189
189 ÷ 3 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
The prime factors of 378 are 2, 3, and 7.
The prime factorization of 378 is: 2 × 33 × 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, 378 is divided by 2 to get 189.
Step 2: Now divide 189 by 3 to get 63.
Step 3: Then divide 63 by 3 to get 21.
Step 4: Divide 21 by 3 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 378 is: 2 × 33 × 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 378: (1, 378), (2, 189), (3, 126), (6, 63), (7, 54), (9, 42), and (18, 21).
Negative factor pairs of 378: (-1, -378), (-2, -189), (-3, -126), (-6, -63), (-7, -54), (-9, -42), and (-18, -21).
Common Mistakes and How to Avoid Them in Factors of 378
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 of every number. Always remember to include 1 and the number itself.
For example, in factors of 378, 1 and 378 are also factors.
Factors of 378 Examples
Problem 1
There are 9 teams and 378 medals. How will they distribute it equally?
They will get 42 medals each.
Explanation
To divide the medals equally, we need to divide the total medals with the number of teams.
378/9 = 42
Problem 2
A garden is rectangular, the length of the garden is 18 meters and the total area is 378 square meters. Find the width?
21 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
378 = 18 × width
To find the value of width, we need to shift 18 to the left side.
378/18 = width
Width = 21.
Problem 3
There are 54 baskets and 378 apples. How many apples will be in each basket?
Each basket will have 7 apples.
Explanation
To find the apples in each basket, divide the total apples with the baskets.
378/54 = 7
Problem 4
In a class, there are 378 students, and 6 groups. How many students are there in each group?
There are 63 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
378/6 = 63
Problem 5
378 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 126 books.
Explanation
Divide total books with shelves.
378/3 = 126
FAQs on Factors of 378
1.What are the factors of 378?
2.Mention the prime factors of 378.
3.Is 378 a multiple of 9?
4.Mention the factor pairs of 378?
5.What is the square of 378?
6.How can children in United States use numbers in everyday life to understand Factors of 378?
7.What are some fun ways kids in United States can practice Factors of 378 with numbers?
8.What role do numbers and Factors of 378 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 378 skills?
Important Glossaries for Factor of 378
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, and 378.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 7 are prime factors of 378.
- 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 378 are (1, 378), (2, 189), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 378 is 2 × 33 × 7.
- Multiple: A multiple is the result of multiplying a number by an integer. For example, 378 is a multiple of 9.
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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.
