Factors of 18: Prime Factorization, Pair Factors and Factor Tree

Factors of 18 are the numbers that on dividing 18 leave zero remainders. 18 have a total of 6 factors of which two are prime numbers. The factors of 18 are positive and negative integers though it doesn’t have any decimal or fraction factors. The factors of 18 are 1, 2, 3, 6, 9 and 18 and the sum of these factors is 39. On dividing 18 by its factors, the resulting quotient will always be an integer.

Also Read: Factors and Multiples

Key Terms: Factor, Factorization, Prime Factorization, Multiples, Integers, Fractions, Quotient, Decimal, Prime Numbers

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What are the Factors of 18

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Factors of a number are defined as the numbers that divide the former one completely with zero as the remainder and an integer as the quotient. 

• Factors of 18 are numbers that when multiplied give 18 as result.
• Factors of 18 are the numbers that divide it completely leaving no remainder.

Factors of 18

The factors of 18 are 6 positive and 6 negative integers.

• Positive Factors: 1, 2, 3, 6, 9, 18
• Negative Factors: -1, -2, -3, -6, -9, -18

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How to find Factors of 18?

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The multiplication method can be used to find the factors of 18. It involves finding pairs of numbers that when multiplied give the required number. The required number is then represented in form of the product of those numbers. 

Also Read: Rational Numbers

Factors of 18 using Multiplication Method

To find factors of 18 using the multiplication method, the first step is performing division on 18 by the numbers 1 to 18. Numbers that divide 18 completely will be its factors. Thus;

• 18 ÷ 1 = 18
• 18 ÷ 2 = 9
• 18 ÷ 3 = 6
• 18 ÷ 6 = 3
• 18 ÷ 9 = 2
• 18 ÷ 18 = 1

Thus the factors of 18 are 1, 2, 3, 6, 9 and 18.

Also Read:

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Prime Factorization of 18

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Prime factorizations of a number is defined as a way of representing the number through the product of its prime factors. To find the prime factorization of 18, follow the given steps.

• Divide 18 with its smallest prime factor. Here, the smallest prime factor of 18 is 2. So, 18 ÷ 2 = 9
• Now, we cannot divide 9 further by 2, so we will move to the next smallest prime factor of 18 which is 3. Thus, 9 ÷ 3 = 3
• Again diving the quotient by 3, 3 ÷ 3 = 1

Prime Factorization of 18

Once the quotient is 1, no further division is needed. Thus, the prime factorization of 18 is

2 × 3 × 3 or 2 × 32

Also Read: Real Numbers

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Factor Tree of 18

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We can also find the factors of 18 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 18 are as follows.

• First, we will split 18 into two factors, let’s that be 2 and 9.
• We will circle out 2 as it is one of the prime factors of 18. 
• Moving on to 9 we will further split it into more factors resulting in 3 and 3.
• Here we have two prime numbers 3 and 3. 

Factor Tree of 18

When we reach prime factors, the tree is complete. Therefore, the prime factors of 18 are: 

2 × 3 × 3

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Pair Factors of 18

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18 have both positive and negative factors and thus it also has both the positive pair factors and the negative pair factors. Both are individually discussed below.

Positive Pair Factor

The table below shows the positive pair factors of 18.

Also Read: Algebra 

Negative Pair Factors

The table below shows the negative pair factors of 18.

Also Read: Geometry

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Solved Examples

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A few solved examples to understand how to use factors of 18 in numerical.

Example 1: Can we divide 18 by 3, 6, 9 and 12 completely?

Solution: The factors of 18 are 1, 2, 3, 6, 9, and 18

Thus only the above-mentioned factors can completely divide 18. 

Hence, 3, 6 and 9 can divide 18 completely but 12 cannot.

Example 2: Find the prime factors of 18.

Solution: Using the prime factorization method, we can find the prime factors of 18.

Following the steps that are mentioned above, the prime factors of 18 are 2 x 3 x 3.

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Things to Remember

• Factors of a number are defined as the numbers that when dividing the former number, leaves zero remainders.
• Factors of 18 are the numbers that when multiplied by another number, generate 18 as the product.
• 18 have 6 positive and 6 negative factors.
• Factors of 18 are 1, 2, 3, 6, 9, and 18.