Factor Calculator – Find Number Factors

A Factor Calculator is a useful tool to determine all the factors of a number. Factors are whole numbers that divide a number without leaving a remainder. This makes it easy to determine factors of a number quickly whether you’re a student trying to learn basic maths, a teacher or someone wanting to solve maths problems.

For example, the factors of 12 would be 1, 2, 3, 4, 6 and 12 since these numbers divide into 12 with no remainder.

Factors play an important role in maths. They are used in multiplication, division, fractions, algebra, number theory and finding the Greatest Common Factor (GCF) or Least Common Multiple (LCM).

This Factor Calculator allows you to determine all of the positive factors of a whole number. This can also be used to find factor pairs and determine whether the number is prime or composite.

Simply input a number, calculate the factors and receive an organised list of factors in seconds. This tool can be used by students, parents, teachers and anyone looking to solve number related problems.

How to Use the Factor Calculator

Using the Factor Calculator is very straightforward. Simply follow the steps below.

1. Input a Number

Type in the positive whole number you want to analyse.

2. Check Input

Make sure it is a valid integer and not a decimal or fraction.

3. Calculate

Click calculate.

4. Find Factors

All positive factors of the number will appear.

5. Check Factor Pairs

If any factors pairs are available they will appear.

For example, if we input 24 into the calculator the factors would be 1, 2, 3, 4, 6, 8, 12 and 24.

Try entering different numbers to see what factors they have and learn more about basic maths.

Factor Calculator Formula

Factors are whole numbers that divide into a number.

Mathematically we can say:

N ÷ d=q

Where,

N is the number

d is the factor

q is the quotient which should be a whole number.

We can also write this as:

N=d x q

If the remainder is zero then d is a factor of N.

Factor Pairs Formula

a x b=N

Where a and b are factors of the number.

Prime Factorisation

A number can be written in terms of prime factors.

For example,

24=2 x 2 x 2 x 3

or

24=2^3 x 3

Prime factorisation can help determine all the positive factors of a number.

Example

Let’s say we want to determine all the factors of 36.

1. Input a Number

Enter 36 into the Factor Calculator.

2. Find Numbers that Divide into 36 with no Remainder

Find all the whole numbers that divide into 36 with no remainder.

36 ÷ 1 = 36

36 ÷ 2 = 18

36 ÷ 3 = 12

36 ÷ 4 = 9

36 ÷ 6 = 6

3. Find Factor Pairs

Factor pairs of 36 are:

1 × 36 = 36

- 2 × 18 = 36

- 3 × 12 = N=d0__

4. List All the Positive Factors

There are 9 factors.

1, 2, 3, 4, 6, 9, 12, 18, 36

All of these divide into 36 with no remainder.

Understanding your Factor Calculator Results

Once you’ve entered a number the factors will be shown in order. Understanding this can help you understand the mathematical relationship between numbers.

Below are the key terms.

• Factors – Whole numbers that divide into the original number.
• Factor Pairs – Two numbers that multiply to give the original number.
• Number of Factors – Total number of positive factors.
• Prime Number – A whole number greater than 1 which only has 2 positive factors. These are 1 and itself.
• Composite Number – A whole number greater than 1 which has more than 2 positive factors.
• Prime Factorisation – A number written in terms of primes.

For example, 13 is a prime number as the only positive factors are 1 and 13. 18 is a composite number as it has positive factors of 1, 2, 3, 6, 9 and 18.

Knowing these can help solve more advanced maths problems.

Factors That Affect the Outcome

The following mathematical factors will affect how many factors there are.

• Size of Number – Larger numbers can have more factors but not necessarily more than all smaller numbers.
• Prime or Composite – Prime numbers only have 2 positive factors. Composite numbers have more than 2 factors.
• Prime Factorisation – The amount of prime factors will determine how many positive factors there are.
• Repeated Prime Factors – Numbers with repeated prime factors can have extra combinations.
• Even or Odd – All positive integers will have 1 and itself as a factor. Even numbers will also have 2 as a factor whereas odd numbers won’t.
• Divisibility Rules – Knowing the rules of divisibility for 2, 3, 5, 9 etc. can help find factors quickly.
• Perfect Square – Perfect squares will have an odd number of positive factors. This is because one of the factor pairs will have 2 of the same numbers.

For example, 36 has a factor pair of 6 x 6 so there are 9 positive factors.

Advantages & Uses of a Factor Calculator

This tool can be very useful when learning maths.

• Save Time – Quickly find all factors.
• Help Students – Helps students learn how to multiply, divide, determine divisibility and number theory.
• Identify Prime Numbers – Determine if the number is prime or composite.
• Find Factor Pairs – Helps to understand how two numbers multiply to give a certain value.
• Simplify Fractions – Find common factors to simplify fractions.
• GCF – Find common factors when calculating the GCF.
• Algebra – Using factorisation to solve equations.
• For example, if we want to simplify 24/36 knowing the GCF is 12 means we can simplify it down to 2/3.

This makes it useful for homework, classwork and self-study.

Accuracy, Assumptions & Limitations

The Factor Calculator uses standard division rules to find factors. When using a positive whole number the answer will be precise.

However, there are some limitations.

It is mainly designed for positive integers.

Decimals and fractions aren’t standard whole number factor questions.

Positive factors will be shown unless negative factors are requested.

0 needs to be treated differently as every non-zero integer divides into 0 meaning there are an infinite amount of integer factors.

Negative integers will have positive and negative factors.

Large numbers could take longer to calculate depending on the method.

For most maths problems at school and in general the results will be accurate for any valid positive whole numbers.

Remember that factors aren’t multiples. Factors divide into a number. Multiples are created by multiplying a number with an integer.

FAQs

1. What is a Factor Calculator?

A Factor Calculator is an online maths tool which can be used to find all the positive whole numbers that divide into a number with no remainder. This can help students, teachers and others quickly solve factor problems.

2. What are factors of a number?

Factors are whole numbers that divide into a number. For example, positive factors of 20 are 1, 2, 4, 5, 10 and 20 as they divide into 20 with no remainder.

3. How do I find all factors of a number?

To find all positive factors divide the original number by consecutive positive integers. Any integers that produce a whole number quotient are factors. To find factor pairs find two numbers that multiply to give the original number.

4. What is the difference between factors and multiples?

Factors divide into a number. Multiples are numbers created by multiplying a number with whole numbers. For example, factors of 12 are 1, 2, 3, 4, 6 and 12. Positive multiples of 12 are 12, 24, 36 and 48.

5. How many factors does a prime number have?

All prime numbers have 2 positive factors. These are 1 and the number itself. For example, 7 is a prime number as it only has 2 positive factors. 1 is neither prime nor composite.

6. What is prime factorisation?

Prime factorisation is when a number is written in terms of prime numbers. For example, prime factorisation of 60 is 2 x 2 x 3 x 5 or N=d1__. This can be useful when finding factors, simplifying fractions and solving GCF problems.

7. Can Factor Calculators find factors of large numbers?

Yes! Factors can be found for many large whole numbers. Depending on the size of the number and the calculation method the calculator might take longer to calculate. Prime factorisation and efficient methods for finding divisors can help make calculations quicker.