Last updated on May 26th, 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 -98, how they are used in real life, and tips to learn them quickly.
The numbers that divide -98 evenly are known as factors of -98.
A factor of -98 is a number that divides the number without remainder.
The positive factors of 98 are 1, 2, 7, 14, 49, and 98.
Therefore, the negative factors of -98 are -1, -2, -7, -14, -49, and -98.
Prime factors of 98: 2 and 7.
Prime factorization of 98: 2 × 7².
The sum of positive factors of 98: 1 + 2 + 7 + 14 + 49 + 98 = 171.
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 -98. Identifying the numbers which are multiplied to get the number -98 is the multiplication method.
Step 1: Multiply -98 by -1, -98 × -1 = 98.
Step 2: Check for other numbers that give -98 after multiplying:
-2 × 49 = -98
-7 × 14 = -98
Therefore, the factor pairs of -98 are: (-1, 98), (-2, 49), (-7, 14).
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 -98 by -1, -98 ÷ -1 = 98.
Step 2: Continue dividing -98 by the numbers until the remainder becomes 0.
-98 ÷ -1 = 98
-98 ÷ -2 = 49
-98 ÷ -7 = 14
Therefore, the factors of -98 are: -1, -2, -7, -14, -49, and -98.
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 -98 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
98 ÷ 2 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factors of 98 are 2 and 7.
The prime factorization of 98 is: 2 × 7².
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 98 is divided by 2 to get 49.
Step 2: Now divide 49 by 7 to get 7.
Step 3: Divide 7 by 7 to get 1. Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 98 is: 2 × 7².
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 98: (1, 98), (2, 49), (7, 14).
Negative factor pairs of -98: (-1, 98), (-2, 49), (-7, 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 14 bags and -98 candies. How will they be divided equally among the bags?
Each bag will get -7 candies.
To divide the candies equally, we need to divide the total candies by the number of bags.
-98/14 = -7
A field is rectangular, the width of the field is -7 meters, and the total area is -98 square meters. Find the length.
14 meters.
To find the length of the field, we use the formula,
Area = length × width
-98 = length × -7
To find the value of length, we need to shift -7 to the left side.
-98/-7 = length
Length = 14.
There are 49 books and -98 boxes. How many books will be in each box?
Each box will have -2 books.
To find the books in each box, divide the total books by the boxes.
-98/49 = -2
In a theater, there are -98 seats and 2 sections. How many seats are there in each section?
There are -49 seats in each section.
Dividing the seats with the total sections, we will get the number of seats in each section.
-98/2 = -49
-98 chairs need to be arranged in 7 rows. How many chairs will go in each row?
Each row has -14 chairs.
Divide total chairs by rows.
-98/7 = -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.