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 -140, how they are used in real life, and tips to learn them quickly.
The numbers that divide -140 evenly are known as factors of -140.
A factor of -140 is a number that divides the number without a remainder.
The factors of -140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140.
Negative factors of -140: -1, -2, -4, -5, -7, -10, -14, -20, -28, -35, -70, and -140.
Prime factors of -140: 2, 5, and 7.
Prime factorization of -140: -1 × 2^2 × 5 × 7.
The sum of factors of 140 (ignoring the negative sign): 1 + 2 + 4 + 5 + 7 + 10 + 14 + 20 + 28 + 35 + 70 + 140 = 336
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 140 (ignoring the negative sign initially). Identifying the numbers which are multiplied to get the number 140 is the multiplication method.
Step 1: Multiply 140 by 1, 140 × 1 = 140.
Step 2: Check for other numbers that give 140 after multiplying
2 × 70 = 140
4 × 35 = 140
5 × 28 = 140
7 × 20 = 140
10 × 14 = 140
Therefore, the positive factor pairs of 140 are: (1, 140), (2, 70), (4, 35), (5, 28), (7, 20), and (10, 14).
For every positive factor, there is a corresponding negative factor for -140.
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 140 by 1, 140 ÷ 1 = 140.
Step 2: Continue dividing 140 by the numbers until the remainder becomes 0.
140 ÷ 1 = 140
140 ÷ 2 = 70
140 ÷ 4 = 35
140 ÷ 5 = 28
140 ÷ 7 = 20
140 ÷ 10 = 14
Therefore, the factors of 140 are: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, and their negative counterparts for -140.
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 -140 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
140 ÷ 2 = 70
70 ÷ 2 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of -140 are 2, 5, and 7.
The prime factorization of -140 is: -1 × 2^2 × 5 × 7.
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 140 is divided by 2 to get 70.
Step 2: Now divide 70 by 2 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 -140 is: -1 × 22 × 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 140: (1, 140), (2, 70), (4, 35), (5, 28), (7, 20), and (10, 14).
Negative factor pairs of -140: (-1, -140), (-2, -70), (-4, -35), (-5, -28), (-7, -20), and (-10, -14).
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 teams and -140 points to distribute equally. How many points will each team get?
Each team will receive -20 points.
To divide the points equally, we need to divide the total points by the number of teams.
-140/7 = -20
A swimming pool is 14 meters long, and the total area is -140 square meters. What is the width of the pool?
-10 meters.
To find the width of the pool, we use the formula,
Area = length × width
-140 = 14 × width
To find the value of width, we need to shift 14 to the left side.
-140/14 = width Width = -10.
There are 20 boxes and -140 candies. How many candies will be in each box?
Each box will have -7 candies.
To find the candies in each box, divide the total candies by the number of boxes.
-140/20 = -7
In a class, there are -140 students, and 28 groups. How many students are there in each group?
There are -5 students in each group.
Dividing the students by the total groups will give the number of students in each group.
-140/28 = -5
-140 books need to be arranged in 10 shelves. How many books will go on each shelf?
Each of the shelves will have -14 books.
Divide total books by shelves.
-140/10 = -14
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.