100 LearnersLast updated on May 26th, 2025
Factors of 392
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 392, how they are used in real life, and tips to learn them quickly.
What are the Factors of 392?
The numbers that divide 392 evenly are known as factors of 392.
A factor of 392 is a number that divides the number without remainder.
The factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, and 392.
Negative factors of 392: -1, -2, -4, -7, -8, -14, -28, -49, -56, -98, -196, and -392.
Prime factors of 392: 2 and 7.
Prime factorization of 392: 23 x 72.
The sum of factors of 392: 1 + 2 + 4 + 7 + 8 + 14 + 28 + 49 + 56 + 98 + 196 + 392 = 855
How to Find Factors of 392?
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 392. Identifying the numbers which are multiplied to get the number 392 is the multiplication method.
Step 1: Multiply 392 by 1, 392 × 1 = 392.
Step 2: Check for other numbers that give 392 after multiplying
2 × 196 = 392
4 × 98 = 392
7 × 56 = 392
8 × 49 = 392
14 × 28 = 392
Therefore, the positive factor pairs of 392 are: (1, 392), (2, 196), (4, 98), (7, 56), (8, 49), and (14, 28).
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 392 by 1, 392 ÷ 1 = 392.
Step 2: Continue dividing 392 by the numbers until the remainder becomes 0.
392 ÷ 1 = 392
392 ÷ 2 = 196
392 ÷ 4 = 98
392 ÷ 7 = 56
392 ÷ 8 = 49
392 ÷ 14 = 28
Therefore, the factors of 392 are: 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392.
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 392 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
392 ÷ 2 = 196
196 ÷ 2 = 98
98 ÷ 2 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factors of 392 are 2 and 7. The prime factorization of 392 is: 23 x 72.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 392 is divided by 2 to get 196.
Step 2: Now divide 196 by 2 to get 98.
Step 3: Then divide 98 by 2 to get 49.
Step 4: Divide 49 by 7 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 392 is: 23 × 72.
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 392: (1, 392), (2, 196), (4, 98), (7, 56), (8, 49), and (14, 28).
Negative factor pairs of 392: (-1, -392), (-2, -196), (-4, -98), (-7, -56), (-8, -49), and (-14, -28).
Common Mistakes and How to Avoid Them in Factors of 392
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 number. Always remember to include 1 and the number itself.
For example, in factors of 392, 1 and 392 is also a factor.
Factors of 392 Examples
Problem 1
There are 28 people and 392 apples. How will they divide them equally?
They will get 14 apples each.
Explanation
To divide the apples equally, we need to divide the total apples with the number of people.
392/28 = 14
Problem 2
A field is rectangular, the length of the field is 14 meters, and the total area is 392 square meters. Find the width?
28 meters.
Explanation
To find the width of the field, we use the formula, Area = length × width 392 = 14 × width
To find the value of width, we need to shift 14 to the left side.
392/14 = width
Width = 28.
Problem 3
There are 14 bags and 392 candies. How many candies will be in each bag?
Each bag will have 28 candies.
Explanation
To find the candies in each bag, divide the total candies by the bags.
392/14 = 28
Problem 4
In a class, there are 392 students, and 7 groups. How many students are there in each group?
There are 56 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
392/7 = 56
Problem 5
392 books need to be arranged in 8 shelves. How many books will go on each shelf?
Each of the shelves has 49 books.
Explanation
Divide total books by shelves.
392/8 = 49
FAQs on Factors of 392
1.What are the factors of 392?
2.Mention the prime factors of 392.
3.Is 392 a multiple of 4?
4.Mention the factor pairs of 392?
5.What is the square of 392?
6.How can children in Canada use numbers in everyday life to understand Factors of 392?
7.What are some fun ways kids in Canada can practice Factors of 392 with numbers?
8.What role do numbers and Factors of 392 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 392 skills?
Important Glossaries for Factors of 392
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, and 392.
- Prime factors: The factors which are prime numbers. For example, 2 and 7 are prime factors of 392.
- 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 392 are (1, 392), (2, 196), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 392 is 23 × 72.
- Multiplication method: A method used to find factors by identifying pairs of numbers that multiply to the original number.
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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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