Last updated on May 26th, 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 -35, how they are used in real life, and tips to learn them quickly.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
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 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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 7 friends and -35 candies. How will they divide it equally?
They will get -5 candies each.
To divide the candies equally, we need to divide the total candies by the number of friends.
-35/7 = -5
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.
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.
There are 5 boxes and -35 apples. How many apples will be in each box?
Each box will have -7 apples.
To find the apples in each box, divide the total apples by the boxes.
-35/5 = -7
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.
Dividing the students by the total groups, we will get the number of students in each group.
35/7 = 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.
Divide total books by shelves.
35/5 = 7
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.
: She loves to read number jokes and games.