Physics Wallah is an Indian edtech platform that provides accessible & comprehensive learning experiences to students from Class 6th to postgraduate level. We also provide extensive NCERT solutions, sample paper, NEET, JEE Mains, BITSAT previous year papers & more such resources to students. Physics Wallah also caters to over 3.5 million registered students and over 78 lakh+ Youtube subscribers with 4.8 rating on its app.
We Stand Out because
We provide students with intensive courses with India’s qualified & experienced faculties & mentors. PW strives to make the learning experience comprehensive and accessible for students of all sections of society. We believe in empowering every single student who couldn't dream of a good career in engineering and medical field earlier.
Our Key Focus Areas
Physics Wallah's main focus is to make the learning experience as economical as possible for all students. With our affordable courses like Lakshya, Udaan and Arjuna and many others, we have been able to provide a platform for lakhs of aspirants. From providing Chemistry, Maths, Physics formula to giving e-books of eminent authors like RD Sharma, RS Aggarwal and Lakhmir Singh, PW focuses on every single student's need for preparation.
What Makes Us Different
Physics Wallah strives to develop a comprehensive pedagogical structure for students, where they get a state-of-the-art learning experience with study material and resources. Apart from catering students preparing for JEE Mains and NEET, PW also provides study material for each state board like Uttar Pradesh, Bihar, and others
The definition of factors in maths is that they are numbers that divide another number exactly, without leaving any remainder. For example, 3 is a factor of 15 because 15 ÷ 3 = 5 with no remainder.
How to find factors of a number?
To find factors of a number, divide it by whole numbers starting from 1. If the number divides exactly with no remainder, then it is a factor. We can also use multiplication pairs to find all the factors.
What are the types of factors in mathematics?
There are different types of factors, like prime factors, which are also prime numbers, and common factors, which are shared between two numbers. The greatest common factor (GCF) is the largest among the common ones.
Why is it important to learn what are factors in maths?
Knowing what is factors in maths helps students understand multiplication and division better. It also helps in solving problems related to HCF, LCM, and simplifying numbers.
What is Factor? – Definition, Types, Examples
What is Factor? It is a number that divides another number exactly without leaving any remainder. Learn the types of factors, their definition, and how to find factors of a number using division and multiplication methods with solved examples.
Shivam Singh25 Jun, 2025
What is Factor?: In mathematics, a factor is a number that divides another number exactly, without leaving any remainder. For example, 2, 3, and 6 are all factors of 6 because they divide it completely. Knowing what is factors in math helps students understand the basic rules of division and multiplication more clearly. It also helps in finding patterns between numbers.
Understanding factors in math is useful in many topics, such as prime numbers, common factors, and multiples. By learning how to find factors of a number, students can solve problems more easily. Keep reading to know about different types of factors with easy-to-understand examples.
What is Factor in Maths?- Understanding Definition of Factors
The definition of factors in math is “They are the whole numbers that can divide another number completely.” These numbers do not leave any remainder after division. For example, 4 is a factor of 20 because when we divide 20 by 4 (20 ÷ 4 = 5), there is no remainder. It is important to note that only positive whole numbers are counted as factors. Fractions, decimals, and zero are not included.
In order to check if a number is a factor, divide the given number by it. If the result is a whole number with no remainder, then it is a factor. Learning what is factors in maths helps students break down numbers into smaller parts and solve maths problems more easily.
How to Find Factors of a Number
To learn how to find factors of a number, we mainly use two methods: the division method and the multiplication method. Both these methods are easy to use and help in finding all the numbers that divide the given number exactly, without leaving any remainder. Let us understand each method with examples to know how to find factors of a number:
Finding Factors Using the Division Method
In the division method, we check which numbers divide the given number without leaving any remainder. These numbers are the factors. Let's look at the example given below to understand it better.
Example: Find the factors of 14 using the division method.
Step 1: To find the factors of 14, we start by dividing it by natural numbers one by one. Start from 1 and go up to 13, as these are the numbers smaller than 14. We need to check which of these numbers divide 14 completely without leaving any remainder.
14 ÷ 1 = 14 (No remainder, so 1 is a factor.)
14 ÷ 2 = 7 (No remainder, so 2 is a factor.)
14 ÷ 3 = 4.66 (Not a whole number, so 3 is not a factor.)
14 ÷ 4 = 3.5 (Not a whole number, so 4 is not a factor.)
14 ÷ 5 = 2.8 (Not a whole number, so 5 is not a factor.)
14 ÷ 6 = 2.33 (Not a whole number, so 6 is not a factor.)
14 ÷ 7 = 2 (No remainder, so 7 is a factor.)
14 ÷ 8 = 1.75 (Not a whole number, so 8 is not a factor.)
14 ÷ 9 = 1.55 (Not a whole number, so 9 is not a factor.)
14 ÷ 10 = 1.4 (Not a whole number, so 10 is not a factor.)
14 ÷ 11 = 1.27 (Not a whole number, so 11 is not a factor.)
14 ÷ 12 = 1.16 (Not a whole number, so 12 is not a factor.)
14 ÷ 13 = 1.07 (Not a whole number, so 13 is not a factor.)
Step 2: Whenever a number divides 14 completely, both the number we used to divide (called the divisor) and the result we get (called the quotient) are factors. For example, 14 ÷ 2 = 7 shows that both 2 and 7 are factors of 14.
Step 3: After checking all the divisions, we find the complete list of numbers that divide 14 exactly. These are 1, 2, 7, and 14.
These are the factors of 14. They come in pairs that multiply to give the original number. The factor pairs of 14 are (1, 14) and (2, 7). The division method helps us find all the factors by simple division.
In the multiplication method, we find pairs of numbers that multiply to give the given number. Each number in the pair is a factor. Find out the examples to know how to find factors of a number using the multiplication method here:
Example: Find the factors of 18 using the multiplication method.
Step 1: Start checking from 1 and find out which numbers can be multiplied with another number to get 18.
1 × 18 = 18
2 × 9 = 18
3 × 6 = 18
Once we reach 4, we stop checking further because any new pair would already have been found in reverse (like 6 × 3 or 9 × 2).
Step 2: Each number in these pairs is a factor of 18. So from the above pairs, we get 1, 2, 3, 6, 9, and 18.
Step 3: List them all in order from smallest to largest: 1, 2, 3, 6, 9, 18.
So, 1, 2, 3, 6, 9, and 18, all are the factors of 18 found by the multiplication method. Just like the division method, the multiplication method also helps us find all factor pairs of a number.
Both the division and multiplication methods are useful and easy to apply. Students can use either method depending on which one they find more comfortable. Knowing how to find factors of a number is an important skill in math, as it builds the base for topics like multiples, common factors, HCF, LCM, and prime factorization.
Factors follow some basic rules in mathematics. Knowing these rules helps students understand how factors work and how to find them easily. Here are some key properties of factors:
1 is the smallest factor of every number. It divides all whole numbers exactly.
The number itself is always its largest factor. For example, 18 is a factor of 18.
The number of factors of any whole number is always limited. This means factors do not go on forever.
A factor is always less than or equal to the number. No factor can be greater than the number it belongs to.
Every number except 0 and 1 has at least two factors—1 and the number itself.
Only multiplication and division are used to find factors of a number. Addition and subtraction are not used for this purpose.
Finding the Number of Factors Using Prime Factorization
To find how many factors a number has, we can use a simple method based on prime factorization. This method helps us count all the factors without listing them one by one.
Step 1: Break the number into its prime factors. That means write it as a multiplication of prime numbers only.
Step 2: Write the prime factors using exponents. For example, if a number has two 2s and one 3, write it as 2² × 3¹.
Step 3: Add 1 to each exponent.
Step 4: Multiply the results from step 3. The final answer gives the total number of factors.
For example: Let’s find the number of factors of 30.
Prime factorization of 30 = 2 × 3 × 5
In exponent form: 2¹ × 3¹ × 5¹
Add 1 to each exponent: (1 + 1), (1 + 1), (1 + 1) → 2, 2, 2
A factor pair is a set of two whole numbers that multiply together to give a specific number. These numbers are called factors, and when they are written in pairs, they help us understand how the number can be formed through multiplication.
Example: Let’s understand it using the number 36.
Step 1: First, list all the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Step 2: Now, group the factors into pairs that give 36 when multiplied:
1 × 36 = 36 (1, 36)
2 × 18 = 36 (2, 18)
3 × 12 = 36 (3, 12)
4 × 9 = 36 (4, 9)
6 × 6 = 36 (6, 6)
So, the positive factor pairs of 36 are (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6).
We can also write negative factor pairs because two negative numbers also multiply to give a positive number.
The negative factor pairs of 36 are (-1, -36), (-2, -18), (-3, -12), (-4, -9), and (-6, -6).
Moreover, it is important for students to note that:
Factor pairs must be whole numbers.
They cannot be decimals or fractions.
For every positive factor pair, there is a matching negative pair.
There are different types of factors in maths that help us understand numbers better. Let's learn about the main types of factors first:
1. Prime Factors
Prime factors are the factors of a number that are also prime numbers. A prime number is a number that has only two factors—1 and itself. For example: Factors of 10 are: 1, 2, 5, and 10. 2 and 5 are prime numbers among them. Therefore, 2 and 5 are the prime factors of 10.
2. Common Factors
Common factors are the numbers that are factors of two or more numbers at the same time. For instance, Factors of 8 are 1, 2, 4, and 8, and Factors of 12 are 1, 2, 3, 4, 6, and 12. So, the common factors of 8 and 12 are 1, 2, and 4.
3. Greatest Common Factor (GCF)
The Greatest Common Factor is the largest number among all the common factors of two or more numbers. From the above example, the common factors of 8 and 12 are 1, 2, and 4. So, the GCF of 8 and 12 is 4.
These types of factors help in solving many maths problems like simplifying fractions, finding LCM and HCF, and understanding number relationships.
Boost Your Child’s Brain Power with Mental Maths Classes By CuriousJr
Is your child also making mistakes while doing maths calculations mentally? This is a common challenge many children face, especially when they depend too much on fingers or calculators for basic sums. These habits can seriously impact their marks in school exams and affect their confidence in maths in future classes.
That’s where CuriousJr’s Mental Maths Online Classes can make a real difference. These mental maths classes help children learn simple tricks and smart methods to solve maths problems quickly and accurately—all in their mind.
With engaging live sessions, achievement badges, and interactive activities, children not only learn but also enjoy math. Here’s what makes the mental maths classes online effective:
Two-teacher model for better attention
Daily practice sessions and homework support
Progress tracking for parents
Fun learning tools to keep kids motivated
Book a demo class today and help your child become sharper, quicker, and more confident in maths.
Talk to a counsellorHave doubts? Our support team will be happy to assist you!
