Factors

# What Are Factors? | How To Find Factor of a Number?

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### What Are Factors? | How To Find Factor of a Number?

Factors are one of the most important concepts to know in mathematics. The concept factors are usually introduced to students in Grades 5 or 6. Factors are nothing but positive numbers that can be divided evenly by a number.

There are multiple methods with the help of which we can find factors of a number.

In this article, we will provide you with all the necessary information on how to find the factors of a given number. Scroll down to find out more.

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**What are Factors in Maths?**

Factors are the numbers that fully divide another number with no remainder in mathematics. They are also known as the numbers you multiply to get another number. Therefore, it means that a factor is a divisor of another number.

In simpler words, if we were to understand a factor, it means that once you multiply a factor by two whole numbers, they will give you a product. Furthermore, after the multiplication, they become divisible by-products.

**Factors Definition**

Factors are numbers that you can use to multiply together with another number to get a different number.

Factors will give you your desired answers after dividing two numbers without a remainder. The fact that a lot of kids forget is that they can be negative or positive, unlike other numbers.

**Factor Example**

Let’s consider the number 8 and find the factor of 8.

8 as a number is the **multiple** of 8 and 1, and 4 and 2. So, that leads to the conclusion that 1,2,4,8 is a factor of 8. When it comes to numbers involving factors to be found or solved for problems, you can see that the numbers used for that are often whole numbers, non-fractions, and positive numbers.

You should also remember the general formula, that is, ab as a product has a and b as factors. The same goes for other numbers too. 2 X 3 = 6 means that 6 has 2 and 3 as factors. Moreover, you can also note that there is no remainder left when 6 is divided by 2 or 3.

**Factors of Prime and Composite Numbers**

Numbers that have 2 factors exactly, such as 1 or the number itself, are prime numbers. Whereas composite numbers are the ones that have more than 2 factors. This means composite numbers can be divided by other numbers other than 1.

So, in conclusion, the prime factor does not have more than 2 factors, and composite numbers have more than 2 factors. Here is an example:

**Properties of a Factor**

Here are the properties of the factor:

- For 1, there is only one factor, which is 1 itself.
- Every factor has a common factor, which is 1.
- Natural numbers are factors of their own.
- Every whole number has 2 or more than 2 factors, except 0 and 1.
- When the number is given to you, the factor is less or equal to that number.
- Factors can be found by using multiplication and division.

**How to Find the Factor of a Number?**

We can find factors of a number using two methods namely – division and multiplication. As said before, you can find factors either by division or multiplication method. Let us see an example of how to find factors for the number 72 using the division and multiplication methods.

### Finding the Factors of 8 Using the Division Method

**Solution:** You have to use numbers that can be divided by 8 with no remainder being left. The numbers less than 8 are 1, 2, 3, 4, 5, 6, and 7. So let us divide the above numbers by 8 and when the remainder is 0, that is a factor and if the remainder is not zero, then it is not a factor of a number.

8 ÷ 1 = 8 (Remainder = 0) |

8 ÷ 2 = 4 (Remainder = 0) |

8 ÷ 3 = 2 (Remainder = 2) |

8 ÷ 4 = 2 (Remainder = 0) |

8 ÷ 5 = 1 (Remainder = 3) |

8 ÷ 6 = 1 (Remainder = 2) |

8 ÷ 7 = 1 (Remainder = 1) |

So the factors of 8 are 1, 2, 4, and 8.

### Finding Factors of 72 Using the Multiplication Method

**Solution:** To find the factors of 72 using the Multiplication method, we need to write down the number 72 as the product of other numbers. The steps to find this are given below:

1 × 72 = 72 | 2 × 36 = 72 |

3 × 24 = 72 | 4 × 18 = 72 |

6 × 12 = 72 | 8 × 9 = 72 |

9 × 8 = 72 | 72 × 1 = 72 |

After seeing this multiplication, we can see that there are repeated numbers, and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72 are the factors of 72.

**Solved Examples **

Here are some solved examples of Factors:

**Question 1: What are the factors of 24?****Solution:** The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24 are the factors. The explanation has been provided in the table below:

1 X 24 = 24 | 2 X 12 = 24 |

3 X 8 = 24 | 6 X 4 = 24 |

4 X 6 = 24 | 8 X 3 = 24 |

12 X 2 = 24 | 24 X 1 = 24. |

**Question 2: What are the factors of 12?****Solution: **The factors of 12 are 1, 2, 3, 4, 6, and 12. We can find factors using the multiplication method as explained in the table below:

1 X 12 = 12 | 2 X 6 = 12 |

3 X 4 = 12 | 4 X 3 = 12 |

6 X 2 = 12 | 12 X 1 = 12 |

**Question 3: What are the factors of 20?Solution:** Here, we will have to do it step-by-step.

**Step 1:**Firstly, we will write every number from 1 to 20.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

**Step 2:**Now, for step 2, we will see the numbers that are divisible by 20, and they should also leave no reminders.

20/1 = 20 (Remainder = 0)

20/2 = 10 (Remainder = 0)

20/3 = 6 (Remainder = 4)

20/4 = 5 (Remainder = 0)

20/5 = 4 (Remainder = 0)

After doing the same with all the numbers to 20, you will get the answer. The factors are 1, 2, 4, 5, 10, and 20.

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**FAQs**

**How do you find a factor?**

All you have to do is take a number and find a factor. And then see all the numbers that will give the same numbers after being multiplied once.

**What are factors and multiples?**

There is a minor difference between factors and multiples. When a number divides with another number exactly with no remainder left, it’s a factor. But when a number is multiplied by another number to get a particular number, it is known as a multiple.

**What are the factors in math?**

Factors are the numbers that give no remainder when divided. They can either be positive or negative. For example, factors of 6 are 1, 2, 3, and 6.

**What is the factor in multiplication?**

When you multiply two whole numbers to get a product, then the numbers that you multiply are the factors of the product. Because they are divisible products.

**What is a factor in algebra?**

A number, or an algebraic expression, that you can divide with another number or expression evenly, and if there is no remainder remaining, then it is a factor in algebra.

**How do you pronounce factors?**

When it comes to pronouncing factors, you just need to say it like this—**Fak-tuhz.**

**What is a multiple in math?**

Multiples are important to know when it comes to factors. They come when you have a number you multiply another with, by an integer, and the numbers you get from them are multiple.

**What is the factor definition for kids?**

When you multiply a number by another number. Then, you get a sum with no remainder. That’s known as factors.

**How to easily find the factors of a number?**

There is one way to quickly find factors and save your time. All you have to do is divide it by the prime number that’s smallest but bigger than 1, then whatever gets into it with no remainder left evenly, you get a factor. Do this same thing again and again until you end up with just 1.

So, that’s all about factors. We hope that this has helped you.

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Written by by

Prerit Jain