123 LearnersLast updated on May 26th, 2025
Factors of -35
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 -35, how they are used in real life, and tips to learn them quickly.
What are the Factors of -35?
The numbers that divide -35 evenly are known as factors of -35.
A factor of -35 is a number that divides the number without remainder.
The factors of -35 are 1, 5, 7, and 35.
Negative factors of -35: -1, -5, -7, and -35.
Prime factors of 35: 5 and 7.
Prime factorization of 35: 5 × 7.
The sum of factors of 35: 1 + 5 + 7 + 35 = 48
How to Find Factors of -35?
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 -35. Identifying the numbers which are multiplied to get the number -35 is the multiplication method.
Step 1: Multiply -35 by 1, -35 × 1 = -35.
Step 2: Check for other numbers that give -35 after multiplying 5 × -7 = -35
7 × -5 = -35
Therefore, the positive factor pairs of -35 are: (1, -35), (5, -7), and (7, -5).
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 -35 by 1, -35 ÷ 1 = -35.
Step 2: Continue dividing -35 by the numbers until the remainder becomes 0.
-35 ÷ 1 = -35
-35 ÷ 5 = -7
-35 ÷ 7 = -5
Therefore, the factors of -35 are: 1, 5, 7, 35.
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 35 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 35 are 5 and 7.
The prime factorization of 35 is: 5 × 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, 35 is divided by 5 to get 7.
Step 2: Now divide 7 by 7 to get 1. Here, 7 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 35 is: 5 × 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 -35: (1, -35), (5, -7), and (7, -5).
Negative factor pairs of -35: (-1, 35), (-5, 7), and (-7, 5).
Common Mistakes and How to Avoid Them in Factors of -35
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 -35, 1 and -35 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 -35 consist of -1, -5, -7, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because -35/1.5 does not result in 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 -35 are prime numbers.
For example, 5 and 7 are the prime factors of 35, but it has other factors like 1 and 35.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 35 as 5 × 7 and missing all the key factors.
Factors of -35 Examples
Problem 1
There are 7 friends and -35 candies. How will they divide it equally?
They will get -5 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
-35/7 = -5
Problem 2
A field is rectangular, the length of the field is 5 meters and the total area is 35 square meters. Find the width?
7 meters.
Explanation
To find the width of the field, we use the formula, Area = length × width
35 = 5 × width
To find the value of width, we need to shift 5 to the left side.
35/5 = width
Width = 7.
Problem 3
There are 5 boxes and -35 apples. How many apples will be in each box?
Each box will have -7 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
-35/5 = -7
Problem 4
In a class, there are 35 students, and 7 groups. How many students are there in each group?
There are 5 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
35/7 = 5
Problem 5
35 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 7 books.
Explanation
Divide total books by shelves.
35/5 = 7
FAQs on Factors of -35
1.What are the factors of -35?
2.Mention the prime factors of 35.
3.Is 35 a multiple of 7?
4.Mention the factor pairs of -35.
5.What is the square of 35?
6.How can children in India use numbers in everyday life to understand Factors of -35?
7.What are some fun ways kids in India can practice Factors of -35 with numbers?
8.What role do numbers and Factors of -35 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of -35 skills?
Important Glossaries for Factor of -35
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -35 are 1, 5, 7, 35, and their negatives.
- Negative factors: Negative numbers that divide the number without leaving a remainder. For example, -1, -5, -7, and -35.
- Prime factors: The factors which are prime numbers. For example, 5 and 7 are prime factors of 35.
- 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 -35 are (1, -35), (5, -7), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 35 is 5 × 7.
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About BrightChamps in India
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.
