# [Maths Class Notes] on Factors of 12 Pdf for Exam

### What are the Factors of 12?

A number when divided by another number and does not leave a remainder then those numbers (divisor) are called factors of that number (dividend). The answer does not change much when talking about the question of what are factors of 12, as the core concept is always the same. It hinges towards complete divisibility when we speak about factors of 12. Here, we are essentially talking about numbers that can divide 12, and also do not result in a remainder. Let us also look at what are the factors of 12, and how many factors in 12 are positive, negative, or prime? You can use different methods to find factors of 12. These are just different representation forms of calculation for the method.

### How to Find the Factors of 12?

When we divide every number with 12 upto that number itself, the numbers that evenly divide with 12 are the factors of 12.

This is a very simple and straightforward method. The entire process takes only 5 steps.

To start off here is step number 1:

Step 1: Consider the number 12

Step 2: Divide it with all the number starting from 1 to 12

Step 3: Capture the results

12/1 = 12

12/2 = 6

12/3 = 4

12/4 = 3

12/5 = 2.4

12/6 = 2

12/7 = 1.7

12/8 = 1.5

12/9 = 1.3

12/10 = 1.2

12/11 = 1.09

12/12 = 1

Step 4: Filter out the positive integer quotient for the above, rejecting the decimals.

Step 5: The factors of 12 are 1, 2, 3, 4, 6, 12.

The factors of 12 also include negative integers. To check how many factors in 12 include negative integers, the above process must be repeated and negative numbers should be considered. This is the easiest way to get the answer to- how many factors in 12 are negative, as there are various other ways which can puzzle you.

### Factor Pairs of 12

These are numbers that when multiplied with each other results in 12.

So here are the factor pairs of 12.

1 x 12 = 12

2 x 6 = 12

3 x 4 = 12

4 x 3 = 12

6 x 2 = 12

12 x 1 = 12

As we had mentioned earlier that factors of 12 also include negative integers. So we will be replacing the above numbers with the minus sign because the product of two negative signs gives a positive result. Let us see how many factors in 12 form factor pairs in the negative series?

-1 x -12 = 12

-2 x -6 = 12

-3 x -4 = 12

-4 x -3 = 12

-6 x -2 = 12

-12 x -1 = 12

In the above pair, we have included pairs like 3 x 4 and 4 x 3. They are the multiples of the individual numbers. Here it is the multiples of 3 and 4.

### Prime Factors of 12

Before heading into prime factors of 12, let us see have a recap about prime numbers and factors? Prime numbers are those that have only two factors, and those are 1 & the number itself. For example, 3 is a prime since it is wholly divisible only by 1 and itself 5.

Factors like stated above, are the numbers, which, when divided with another number doesn’t leave a remainder.

So, below we can see the process to find the prime factors of 12:

Step 1:- Take 12 and divide it by the smallest prime number

12 / 2 = 6

Step 2:- Keeping dividing the result with small prime numbers

6 / 2 = 3

Step 3:- Continue the process, until the result is 1

3 / 3 = 1

Step 4:- In conclusion, we get the prime factors of 12 as

2, 2, 3

To reconfirm the values of the prime factors of 12, you can multiply the prime factors and the resulting answer should be a 12.

2 x 2 x 3 = 12

### What are the Factors of 12?

After following the steps to find the factors of 12, we can list down all the factors. Including the positive as well as negative integers. The following integers are the factors of 12:

1, 2, 3, 4, 6, and 12

-1, -2, -3, -4, -6, and -12

In general, you can find the factors of any number in a similar manner. While the number gets larger the methods will change a little bit. But until a certain range of numbers, the above method is used.

### Fun Facts

• You will never have factors as decimals and fractions, they are always whole numbers or integers.

• 2 is the common factor for all even numbers.

• For a square number, the number of factors is odd when for most other numbers is even.

• The number 5 is present as a factor in numbers that ends with 5 like 15, 25, 35.

• Numbers that end with 0 have 2, 5, and 10 as their factors like 10, 20, 30.

### Solved Examples

1. Find the Factors of 24?

To find the factors of 24, we will see which numbers divide it completely.

24/1 = 24

24/2= 12

24/3= 8

24/4=6

24/6=4

24/8=3

24/12= 2

24/24= 1

So, positive factors of 24 are as follows= 1,2,3,4,6,8,12,24.

1. Find factor of 36?

To find the factors of 36, we will follow the process used for 24.

36/1= 36

36/2= 18

36/3 = 12

36/4 = 9

36/6 = 6

36/9 = 4

36/12= 3

36/18= 2

36/36= 1

So, positive factors of 36 are as follows= 1, 2, 3, 4, 6, 9, 12, 18, 36.