163 LearnersLast updated on May 26th, 2025
Factors of 98
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 the tips to learn them quickly.
What are the Factors of 98?
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 factors of 98 are 1, 2, 7, 14, 49, and 98.
Negative factors of 98: -1, -2, -7, -14, -49, and -98.
Prime factors of 98: 2 and 7.
Prime factorization of 98: 2 × 7².
The sum of factors of 98: 1 + 2 + 7 + 14 + 49 + 98 = 171
How to Find Factors of 98?
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 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 positive factor pairs of 98 are: (1, 98), (2, 49), (7, 14).
All these factor pairs result in 98. For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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, 98.
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 98 divide the number to break it down into the multiplication form of prime factors till 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.
Factor Tree
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, we reach 1, and all the factors are prime numbers. 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).
Common Mistakes and How to Avoid Them in Factors of 98
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 98, 1 and 98 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors. For example, the factors of 98 consist of -1, -2, -7, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor. For example, thinking 1.5 as a factor because 98/1.5 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 98 are prime numbers. For example, 2 and 7 are the prime factors of 98, but it has other factors like 14 and 49.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors. For example, not breaking 98 as 2 × 7² and missing all the key factors.
Factors of 98 Examples
Problem 1
There are 49 apples and 98 chocolates. How will they distribute the chocolates equally among the apples?
They will get 2 chocolates each.
Explanation
To distribute the chocolates equally,
we need to divide the total chocolates by the number of apples.
98/49 = 2
Problem 2
A rectangular garden has a length of 7 meters and a total area of 98 square meters. Find the width?
14 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
98 = 7 × width
To find the value of width, we need to shift 7 to the left side.
98/7 = width
Width = 14.
Problem 3
There are 14 baskets, and 98 mangoes. How many mangoes will be in each basket?
Each basket will have 7 mangoes.
Explanation
To find the mangoes in each basket,
divide the total mangoes by the baskets.
98/14 = 7
Problem 4
In a class, there are 98 students, and 7 groups. How many students are there in each group?
There are 14 students in each group.
Explanation
Dividing the students by the total groups,
we will get the number of students in each group.
98/7 = 14
Problem 5
98 books need to be arranged on 2 shelves. How many books will go on each shelf?
Each of the shelves has 49 books.
Explanation
Divide total books by shelves.
98/2 = 49
FAQs on Factors of 98
1.What are the factors of 98?
2.Mention the prime factors of 98.
3.Is 98 a multiple of 7?
4.Mention the factor pairs of 98?
5.What is the square of 98?
Important Glossaries for Factor of 98
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 98 are 1, 2, 7, 14, 49, and 98.
- Prime factors: The factors which are prime numbers. For example, 2 and 7 are prime factors of 98.
- 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 98 are (1, 98), (2, 49), etc.
- Prime factorization: Breaking down a number into its prime factors. For 98, it is 2 × 7².
- Multiplication method: A way to find factors by identifying pairs of numbers that multiply to the original number. For example, using pairs like (7, 14) for 98.
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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.
