# Factors of 12

Factors of 12 are 1, 2, 3, 4, 6, and 12

#### How to find factors of a number

 1.   Find factors of 12 using Division Method 2.   Find factors of 12 using Prime Factorization 3.   Find factors of 12 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 12

• Divide 12 by 1: 12 ÷ 1 : Remainder = 0
• Divide 12 by 2: 12 ÷ 2 : Remainder = 0
• Divide 12 by 3: 12 ÷ 3 : Remainder = 0
• Divide 12 by 4: 12 ÷ 4 : Remainder = 0
• Divide 12 by 6: 12 ÷ 6 : Remainder = 0
• Divide 12 by 12: 12 ÷ 12 : Remainder = 0

Hence, Factors of 12 are 1, 2, 3, 4, 6, and 12

#### 2. Steps to find factors of 12 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 12 using the division method, follow these steps:

• Step 1. Start dividing 12 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 12, which is 2. Divide 12 by 2 to obtain the quotient (6).
12 ÷ 2 = 6
• Step 3. Repeat step 1 with the obtained quotient (6).
6 ÷ 2 = 3
3 ÷ 3 = 1

So, the prime factorization of 12 is, 12 = 2 x 2 x 3.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 12 as shown below:

So, the prime factorization of 12 is, 12 = 2 x 2 x 3.

#### 3. Find factors of 12 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 12 would be the two numbers which, when multiplied, give 12 as the result.

The following table represents the calculation of factors of 12 in pairs:

Factor Pair Pair Factorization
1 and 12 1 x 12 = 12
2 and 6 2 x 6 = 12
3 and 4 3 x 4 = 12

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 12. They are called negative pair factors.

Hence, the negative pairs of 12 would be ( -1 , -12 ) , ( -2 , -6 ) and ( -3 , -4 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 12 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 12.
• Every number is a factor of zero (0), since 12 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 6, 12 are exact divisors of 12.
• Factors of 12 are 1, 2, 3, 4, 6, 12. Each factor divides 12 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 12 are all less than or equal to 12.

• What are the prime factors of 12?

The factors of 12 are 1, 2, 3, 4, 6, 12.
Prime factors of 12 are 2, 2, 3.

• What two numbers make 12?

Two numbers that make 12 are 2 and 6.

• What is the greatest prime factors of 12?

The greatest prime factor of 12 is 3.

• What are factors of 12?

Factors of 12 are 1, 2, 3, 4, 6, 12.

• How do you find factors of a negative number? ( eg. -12 )?

Factors of -12 are -1, -2, -3, -4, -6, -12.

• What are five multiples of 12?

First five multiples of 12 are 24, 36, 48, 60, 72.

• Write some multiples of 12?

First five multiples of 12 are 24, 36, 48, 60.

• Is 12 a perfect square?

No 12 is not a perfect square.

• What two numbers make 12?

Two numbers that make 12 are 2 and 6.

#### Examples of Factors

What is prime factorization of 12?

Prime factorization of 12 is 2 x 2 x 3 = 22 x 3.

Sammy is puzzled while calculating the prime factors of 12. Can you help him find them?

Factors of 12 are 1, 2, 3, 4, 6, 12.
Prime factors of 12 are 2, 2, 3

Kevin has been asked to write 5 factor(s) of 12. Can you predict the answer?

5 factor(s) of 12 are 1, 2, 3, 4, 6.

Joey wants to write all the prime factors of 12 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 12 are 2, 2, 3.
So in exponential form it can be written as 22 x 3.

How many factors are there for 12?

Factors of 12 are 1, 2, 3, 4, 6, 12.
So there are in total 6 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 12? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 12.
Negative factors are -1, -2, -3, -4, -6, -12.

Can you help Rubel to find out the product of the even factors of 12?

Factors of 12 are 1, 2, 3, 4, 6, 12.
Even factors of 12 are 2, 4, 6, 12.
Hence, product of even factors of 12 is; 2 x 4 x 6 x 12 = 576.