124 LearnersLast updated on May 26th, 2025
Factors of 350
Factors are the numbers that divide any given number evenly without a 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 350, how they are used in real life, and tips to learn them quickly.
What are the Factors of 350?
The numbers that divide 350 evenly are known as factors of 350.
A factor of 350 is a number that divides the number without a remainder.
The factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, and 350.
Negative factors of 350: -1, -2, -5, -7, -10, -14, -25, -35, -50, -70, -175, and -350.
Prime factors of 350: 2, 5, and 7.
Prime factorization of 350: 2 × 52 × 7.
The sum of factors of 350: 1 + 2 + 5 + 7 + 10 + 14 + 25 + 35 + 50 + 70 + 175 + 350 = 744
How to Find Factors of 350?
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 350. Identifying the numbers which are multiplied to get the number 350 is the multiplication method.
Step 1: Multiply 350 by 1, 350 × 1 = 350.
Step 2: Check for other numbers that give 350 after multiplying
2 × 175 = 350
5 × 70 = 350
7 × 50 = 350
10 × 35 = 350
14 × 25 = 350
Therefore, the positive factor pairs of 350 are: (1, 350), (2, 175), (5, 70), (7, 50), (10, 35), (14, 25).
All these factor pairs result in 350.
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 350 by 1, 350 ÷ 1 = 350.
Step 2: Continue dividing 350 by the numbers until the remainder becomes 0.
350 ÷ 1 = 350
350 ÷ 2 = 175
350 ÷ 5 = 70
350 ÷ 7 = 50
350 ÷ 10 = 35
350 ÷ 14 = 25
Therefore, the factors of 350 are: 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 350 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
350 ÷ 2 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 350 are 2, 5, and 7.
The prime factorization of 350 is: 2 × 52 × 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, 350 is divided by 2 to get 175.
Step 2: Now divide 175 by 5 to get 35.
Step 3: Then divide 35 by 5 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 350 is: 2 × 52 × 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 350: (1, 350), (2, 175), (5, 70), (7, 50), (10, 35), (14, 25).
Negative factor pairs of 350: (-1, -350), (-2, -175), (-5, -70), (-7, -50), (-10, -35), (-14, -25).
Common Mistakes and How to Avoid Them in Factors of 350
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 350, 1 and 350 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 350 consist of -1, -2, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 350/1.5 = 233.333, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 350 are prime numbers.
For example, 2, 5, and 7 are the prime factors of 350, but it has other factors like 10, 14.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 350 as 2 × 5^2 × 7 and missing all the key factors.
Factors of 350 Examples
Problem 1
There are 35 participants in a contest and 350 points available. How many points will each participant get if distributed equally?
They will get 10 points each.
Explanation
To distribute the points equally, we need to divide the total points with the number of participants.
350/35 = 10
Problem 2
A garden is rectangular, the width of the garden is 10 meters and the total area is 350 square meters. Find the length.
35 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
350 = length × 10
To find the value of length, we need to shift 10 to the left side.
350/10 = length Length = 35.
Problem 3
There are 14 boxes and 350 balloons. How many balloons will be in each box?
Each box will have 25 balloons.
Explanation
To find the balloons in each box, divide the total balloons with the boxes.
350/14 = 25
Problem 4
In a school, there are 350 students, and 5 buses. How many students are there in each bus?
There are 70 students in each bus.
Explanation
Dividing the students with the total buses, we will get the number of students in each bus.
350/5 = 70
Problem 5
350 chairs need to be arranged in 7 rows. How many chairs will go in each row?
Each row has 50 chairs.
Explanation
Divide total chairs with rows.
350/7 = 50
FAQs on Factors of 350
1.What are the factors of 350?
2.Mention the prime factors of 350.
3.Is 350 a multiple of 7?
4.Mention the factor pairs of 350?
5.What is the square of 350?
6.How can children in India use numbers in everyday life to understand Factors of 350?
7.What are some fun ways kids in India can practice Factors of 350 with numbers?
8.What role do numbers and Factors of 350 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 350 skills?
Important Glossaries for Factor of 350
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, and 350.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 7 are prime factors of 350.
- 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 350 are (1, 350), (2, 175), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 350 is 2 × 52 × 7.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 350 is a multiple of 7.
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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.
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