123 LearnersLast updated on May 26th, 2025
Factors of 370
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 370, how they are used in real life, and tips to learn them quickly.
What are the Factors of 370?
The numbers that divide 370 evenly are known as factors of 370. A factor of 370 is a number that divides the number without remainder.
The factors of 370 are 1, 2, 5, 10, 37, 74, 185, and 370.
Negative factors of 370: -1, -2, -5, -10, -37, -74, -185, and -370.
Prime factors of 370: 2, 5, and 37.
Prime factorization of 370: 2 × 5 × 37.
The sum of factors of 370: 1 + 2 + 5 + 10 + 37 + 74 + 185 + 370 = 684
How to Find Factors of 370?
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 370. Identifying the numbers which are multiplied to get the number 370 is the multiplication method.
Step 1: Multiply 370 by 1, 370 × 1 = 370.
Step 2: Check for other numbers that give 370 after multiplying 2 × 185 = 370 5 × 74 = 370 10 × 37 = 370
Therefore, the positive factor pairs of 370 are: (1, 370), (2, 185), (5, 74), (10, 37). 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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 370 by 1, 370 ÷ 1 = 370.
Step 2: Continue dividing 370 by the numbers until the remainder becomes 0.
370 ÷ 1 = 370
370 ÷ 2 = 185
370 ÷ 5 = 74
370 ÷ 10 = 37
Therefore, the factors of 370 are: 1, 2, 5, 10, 37, 74, 185, 370.
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 370 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
370 ÷ 2 = 185
185 ÷ 5 = 37
37 ÷ 37 = 1
The prime factors of 370 are 2, 5, and 37.
The prime factorization of 370 is: 2 × 5 × 37.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 370 is divided by 2 to get 185.
Step 2: Now divide 185 by 5 to get 37.
Step 3: 37 is a prime number and cannot be divided further. So, the prime factorization of 370 is: 2 × 5 × 37.
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 370: (1, 370), (2, 185), (5, 74), (10, 37).
Negative factor pairs of 370: (-1, -370), (-2, -185), (-5, -74), (-10, -37).
Common Mistakes and How to Avoid Them in Factors of 370
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 as 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 370, 1 and 370 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 370 include -1, -2, -5, etc.
Mistake 3
Including Fractions
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor for 370 would be incorrect because 370/1.5 is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not just primes.
For example, thinking all the factors of 370 are prime numbers. While 2, 5, and 37 are the prime factors of 370, it has other factors like 10, 185.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing incorrect factors.
For example, not breaking 370 as 2 × 5 × 37 and missing all the key factors.
Factors of 370 Examples
Problem 1
There are 74 students and 370 pencils. How will they distribute them equally among themselves?
Each student will get 5 pencils.
Explanation
To distribute the pencils equally, we need to divide the total pencils by the number of students.
370/74 = 5
Problem 2
A garden is rectangular, the length of the garden is 37 meters and the total area is 370 square meters. Find the width.
10 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
370 = 37 × width
To find the value of width, we need to shift 37 to the left side.
370/37 = width
Width = 10.
Problem 3
There are 185 apples and 370 baskets. How many apples will be in each basket if distributed equally?
Each basket will have 2 apples.
Explanation
To find the apples in each basket, divide the total apples by the number of baskets.
370/185 = 2
Problem 4
In a class, there are 370 students, and they need to form groups of 10. How many students will be there in each group?
There will be 37 groups.
Explanation
Dividing the students with the group size gives the number of groups.
370/10 = 37
Problem 5
370 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves will have 74 books.
Explanation
Divide the total books by the number of shelves.
370/5 = 74
FAQs on Factors of 370
1.What are the factors of 370?
2.Mention the prime factors of 370.
3.Is 370 a multiple of 10?
4.Mention the factor pairs of 370.
5.What is the square of 370?
6.How can children in United States use numbers in everyday life to understand Factors of 370?
7.What are some fun ways kids in United States can practice Factors of 370 with numbers?
8.What role do numbers and Factors of 370 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 370 skills?
Important Glossaries for Factors of 370
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 370 are 1, 2, 5, 10, 37, 74, 185, and 370.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 37 are prime factors of 370.
- 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 370 are (1, 370), (2, 185), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For 370, it is 2 × 5 × 37.
- Multiplication Method: A method of finding factors by identifying pairs of numbers that multiply to give the original number, such as 10 × 37 = 370.
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About BrightChamps in United States
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.
