Factors of 12: Prime Factorization, Pair Factors and Factor Tree

Factors of 12 are the numbers that on dividing 12 leave zero remainders. 12 have a total of 6 factors of which three are prime numbers. The factors of 12 are positive and negative integers though it doesn’t have any decimal or fraction factors. The factors of 12 are 1, 2, 3, 4, 6 and 12. The total sum of factors of 12 is 28. 

Also Read: Rational Numbers

Key Terms: Factors, Prime Numbers, Prime Factorization, Remainders, Whole Numbers, Decimals, Fractions, Integers

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What are the Factors of 12

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The factor of a number is defined as another number that divides the former completely with zero as the remainder.

• Factors of 12 are the numbers that divide it completely leaving no remainder.
• Factors of 12 are numbers that when multiplied give 12 as result.

Factors of 12

The factors of 12 are 6 positive and 6 negative integers.

• Positive Factors: 1, 2, 3, 4, 6, 12
• Negative Factors: -1, -2, -3, -4, -6, -12

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How to find Factors of 12?

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Factors of 12 can be found using the multiplication method. It is a method which involves finding pairs of numbers that when multiplied give the required number. The number is then represented in form of the product of those numbers. 

Also Read: Divisor

Factors of 12 using Multiplication Method

First to find factors of 12 using the multiplication method, we need to divide 12 by the numbers 1 to 9. Numbers that divide 12 completely will be its factors. Thus;

• 12 ÷ 1 = 12
• 12 ÷ 2 = 6
• 12 ÷ 3 = 4
• 12 ÷ 4 = 3
• 12 ÷ 6 = 2
• 12 ÷ 12 = 1

Thus the factors of 12 are 1, 2, 3, 4, 6 and 12.

Also Read:

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Prime Factorization of 12

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Prime factorizations of a number is a way of representing the number through the product of its prime factors. To find the prime factorization of 12 follow the given steps.

• Divide 12 with its smallest prime factor. Here, the smallest prime factor of 12 is 2. So, 12 ÷ 2 = 6
• Repeated division of obtained quotient by 2 until we get a number that is not divisible by 2. Dividing 12 again by 2, 6 ÷ 2 = 3
• Now, dividing the quotient by 3, 3 ÷ 3 = 1

Prime Factorization of 12

Once the quotient is 1, no further division is needed. Thus, the prime factorization of 12 is

2 × 2 × 3 or 2² × 3

Also Read: Real Numbers

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Factor Tree of 12

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Another way of finding the factors of 12 is through the factor tree. The factor tree of any number is drawn by factorization until we reach its prime factors. The steps to draw a factor tree of 12 are as follows.

• The first step is to split 12 into two factors, let’s that be 2 and 6.
• We will circle out 2 as it is one of the prime factors of 12. 
• Moving on to 6 we will further split it into more factors resulting in 2 and 3.
• Here we have two prime numbers 2 and 3. 

Factor of 12

When we reach prime factors, the tree is complete. Therefore, the prime factors of 12 are: 

2 × 2 × 3

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Pair Factors of 12

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There are two types of pair factors: Positive pair factors and Negative pair factors. 12 has both types of pair factors since it has both positive and negative factors. Both are individually discussed below.

Positive Pair Factor

The table below shows the positive pair factors of 12.

Also Read: Algebra 

Negative Pair Factors

The table below shows the negative pair factors of 12.

Also Read: Geometry

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Solved Examples

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A few solved examples to understand how to use factors of 12 in numerical.

Example 1: Can we divide 12 by 3, 6, 9 and 10 completely?

Solution: The factors of 12 are 1, 2, 3, 4, 6, and 12.

Thus only the above-mentioned factors can completely divide 12. 

Hence, 3 and 6 can divide 12 completely but 9 and 10 cannot.

Example 2: Find the prime factors of 12.

Solution: Using the prime factorization method, we can find the prime factors of 12.

Following the steps that are mentioned above, the prime factors of 12 are 2 x 2 x 3.

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Things to Remember

• Factors of a number are defined as the numbers that when dividing the former number, leave zero remainders.
• Factors of 12 are the numbers that when multiplied by another number, give 12 as result.
• 12 have 6 positive and 6 negative factors.
• Factors of 12 are 1, 2, 3, 4, 6, and 12.