Factors of 12: Definition, Prime Factorization, Factor Tree

Factors are the numbers that you divide and the remainder comes as zero. Let’s consider the examples of 2 and 8. How would you know if the number 2 is a factor of 8? So when you divide 2 by 8 and the remainder comes as zero, then it is a factor of 8. In this case, 2 is a factor of 8. Let’s see what are the factors of 12 along with the definition, Prime factorization and factor tree of 12. 

Definition of Factors

Imagine you have a certain number of objects, and you want to divide them into equal groups with no leftovers. The factors of the number of objects tell you how many groups you can create and how many objects would be in each group.

For example, if you have 12 apples and want to share them equally among your friends, you could divide them into groups of 1 (each friend gets 1 apple), 2 (each friend gets 2 apples), 3 (each friend gets 3 apples), 4 (each friend gets 3 apples), 6 (each friend gets 2 apples), or 12 (each friend gets all the apples). In this case, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Also Read: Factors of 20

Factors of 12 By Prime Factorization Method

Imagine breaking down a number into its most basic building blocks, like Legos!

In math, these building blocks for whole numbers are called Prime numbers. Prime numbers are only divisible by 1 and themselves.

Prime factorization is a way of figuring out which prime numbers, when multiplied together, make up a specific number.

Let’s take the smallest number you know. 

Say 1,

Now we will see what we can divide by 1 to get a remainder of 0. We already know that 1 is divided by all the numbers with the remainder zero, so 1 will be a factor of 12. 

Now say 2,

6 times 2 is 12 which means it is divided by 12 and the remainder is 0. So 6 and 2 both are factors of 12. 

Now it’s 3,

Recall the table of 3. 4 times 3 is 12, so you must already know by now that the remainder will be 0 when you divide 3/12. So here 3 and 4 will be the factors of 12. 

What is the Factor Tree of 12?

Another easy way to find out the factors of any given number is by using the factor tree.

The Factor tree of 12:

     12

     /   \

    2     6

    / \

         3   2

Step 1: First, divide 12 into two components. Take numbers 2 and 6.

Step 2: Examine these factors to determine whether or not they are prime.

Step 3: We circle 2 as one of the prime factors of 12 because it is a prime number. The composite number 6 is the next one we divide into additional factors. Put otherwise, we keep factorizing 6 and dividing it into branches until we arrive at a prime number. We divide 6 into 3 and 2, then.

Step 4: At this point, the only prime numbers we have left are 2 and 3. Since we are aware that they cannot be further factorized, we circle them. The factor tree finishes here.

Therefore, the Prime factors of 12 = 2 × 3 × 2

Also Read- All You Need to Know About HCF and LCM

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