Factors of -175
2026-02-28 09:06 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-minus-175

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Last updated on December 12, 2025

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 -175, how they are used in real life, and the tips to learn them quickly.

What are the Factors of -175?

The numbers that divide -175 evenly are known as factors of -175.

A factor of -175 is a number that divides the number without remainder.

The factors of -175 are -1, 1, -5, 5, -7, 7, -25, 25, -35, 35, -175, and 175.

Negative factors of -175: -1, -5, -7, -25, -35, -175.

Prime factors of 175: 5 and 7.

Prime factorization of 175: (52 times 7).

The sum of the positive factors of 175: 1 + 5 + 7 + 25 + 35 + 175 = 248

How to Find Factors of -175?

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 175. Identifying the numbers which are multiplied to get the number 175 is the multiplication method.

Step 1: Multiply 175 by 1, 175 × 1 = 175.

Step 2: Check for other numbers that give 175 after multiplying: (5 \times 35 = 175) (7 times 25 = 175)

Therefore, the positive factor pairs of 175 are: (1, 175), (5, 35), (7, 25).

All these factor pairs result in 175. 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 the simple division method

Step 1: Divide -175 by 1, -175 ÷ 1 = -175.

Step 2: Continue dividing -175 by the numbers until the remainder becomes 0. (-175 ÷ 1 = -175) (-175 ÷ 5 = -35) (-175 ÷ 7 = -25)

Therefore, the factors of -175 are: -1, 1, -5, 5, -7, 7, -25, 25, -35, 35, -175, 175.

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: In this process, prime factors of 175 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

175 ÷ 5 = 35

35 ÷ 5 = 7

7 ÷ 7 = 1

The prime factors of 175 are 5 and 7.

The prime factorization of 175 is: (52 times 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, 175 is divided by 5 to get 35.

Step 2: Now divide 35 by 5 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 175 is: (52 times 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 175: (1, 175), (5, 35), and (7, 25).

Negative factor pairs of -175: (-1, -175), (-5, -35), and (-7, -25).

Common Mistakes and How to Avoid Them in Factors of -175

Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.

Problem 1

There are 7 teams and -175 points. How will they share it equally?

Okay, lets begin

They will get -25 points each.

Explanation

To divide the points equally, we need to divide the total points by the number of teams. (-175/7 = -25)

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Problem 2

A garden is rectangular, the length of the garden is 5 meters, and the total area is 175 square meters. Find the width.

Okay, lets begin

35 meters.

Explanation

To find the width of the garden, we use the formula,

Area = length × width

175 = 5 × width

To find the value of width, we need to shift 5 to the left side.

175/5 = width Width = 35.

Well explained 👍

Problem 3

There are 25 boxes and 175 marbles. How many marbles will be in each box?

Okay, lets begin

Each box will have 7 marbles.

Explanation

To find the marbles in each box, divide the total marbles by the boxes.

175/25 = 7

Well explained 👍

Problem 4

In a tournament, there are 175 players, and 5 teams. How many players are there in each team?

Okay, lets begin

There are 35 players in each team.

Explanation

Dividing the players by the total teams, we will get the number of players in each team.

175/5 = 35

Well explained 👍

Problem 5

175 pages need to be arranged in 5 folders. How many pages will go in each folder?

Okay, lets begin

Each of the folders has 35 pages.

Explanation

Divide total pages by folders.

175/5 = 35

Well explained 👍

FAQs on Factors of -175

1.What are the factors of -175?

-1, 1, -5, 5, -7, 7, -25, 25, -35, 35, -175, 175 are the factors of -175.

2.Mention the prime factors of 175.

The prime factors of 175 are \(5^2 \times 7\).

3.Is 175 a multiple of 5?

4.Mention the factor pairs of -175?

(-1, -175), (-5, -35), (-7, -25) are the factor pairs of -175.

5.What is the square of 175?

Important Glossaries for Factor of -175

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -175 are -1, 1, -5, 5, -7, 7, -25, 25, -35, 35, -175, 175.
     
  • Prime factors: The factors which are prime numbers. For example, 5 and 7 are prime factors of 175.
     
  • 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 175 are (1, 175), (5, 35), etc.
     
  • Negative factors: Factors that are negative integers. For example, -1, -5, -7 are negative factors of -175.
     
  • Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 175 is (52 times 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.