Factors of 350
2026-02-28 08:45 Diff
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Last updated on December 11, 2025

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

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.

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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: 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.

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Problem 1

There are 35 participants in a contest and 350 points available. How many points will each participant get if distributed equally?

Okay, lets begin

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

Well explained 👍

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.

Okay, lets begin

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.

Well explained 👍

Problem 3

There are 14 boxes and 350 balloons. How many balloons will be in each box?

Okay, lets begin

Each box will have 25 balloons.

Explanation

To find the balloons in each box, divide the total balloons with the boxes.

350/14 = 25

Well explained 👍

Problem 4

In a school, there are 350 students, and 5 buses. How many students are there in each bus?

Okay, lets begin

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

Well explained 👍

Problem 5

350 chairs need to be arranged in 7 rows. How many chairs will go in each row?

Okay, lets begin

Each row has 50 chairs.

Explanation

Divide total chairs with rows.

350/7 = 50

Well explained 👍

FAQs on Factors of 350

1.What are the factors of 350?

1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350 are the factors of 350.

2.Mention the prime factors of 350.

The prime factors of 350 are 2 × 5^2 × 7.

3.Is 350 a multiple of 7?

4.Mention the factor pairs of 350?

(1, 350), (2, 175), (5, 70), (7, 50), (10, 35), (14, 25) are the factor pairs of 350.

5.What is the square of 350?

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.

Fun Fact

: She loves to read number jokes and games.