121 LearnersLast updated on May 26th, 2025
Factors of -175
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.
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
- Using factor tree
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.
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 -175, -1 and 175 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 -175 consist of -1, -5, -7, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because -175/1.5 = -116.666, 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 -175 are prime numbers.
For example, 5 and 7 are the prime factors of 175, but it has other factors like 25, 35.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 175 as \(5^2 \times 7\) and missing all the key factors.
Factors of -175 Examples
Problem 1
There are 7 teams and -175 points. How will they share it equally?
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)
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.
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.
Problem 3
There are 25 boxes and 175 marbles. How many marbles will be in each box?
Each box will have 7 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the boxes.
175/25 = 7
Problem 4
In a tournament, there are 175 players, and 5 teams. How many players are there in each team?
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
Problem 5
175 pages need to be arranged in 5 folders. How many pages will go in each folder?
Each of the folders has 35 pages.
Explanation
Divide total pages by folders.
175/5 = 35
FAQs on Factors of -175
1.What are the factors of -175?
2.Mention the prime factors of 175.
3.Is 175 a multiple of 5?
4.Mention the factor pairs of -175?
5.What is the square of 175?
6.How can children in Vietnam use numbers in everyday life to understand Factors of -175?
7.What are some fun ways kids in Vietnam can practice Factors of -175 with numbers?
8.What role do numbers and Factors of -175 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of -175 skills?
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).
Explore More numbers
About BrightChamps in Vietnam
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.
