Factors of 18

Factors of 18 are the list of integers that can be evenly divided into 18. It has a total of 6 factors of which 18 is the biggest factor and the positive factors of 18 are 1, 2, 3, 6, 9, and 18. The Pair Factors of 18 are (1, 18), (2, 9), and (3, 6) and its Prime Factors are 1, 2, 3, 6, 9, 18.

• Factors of 18: 1, 2, 3, 6, 9 and 18
• Negative Factors of 18: -1, -2, -3, -6, -9 and -18
• Prime Factors of 18: 2, 3
• Prime Factorization of 18: 2 × 3 × 3 = 2 × 3²
• Sum of Factors of 18: 39

Let us explore more about factors of 18 and ways to find them.

What Are the Factors of 18?

Factors of a number are the numbers that divide the given number exactly without any remainder. According to the definition of factors, the factors of 18 are 1, 2, 3, 6, 9, and 18. So,18 is a composite number as it has more factors other than 1 and itself.

We can use different methods like the divisibility test, prime factorization, and the upside-down division method to calculate the factors of 18. In prime factorization, we express 18 as a product of its prime factors, and in the division method, we see which numbers divide 18 exactly without a remainder.

Let us calculate factors of 18 using the following two methods:

• Factors of 18 by prime factorization factor tree method
• Factors of 18 by upside-down division method

Prime Factorization By Upside-Down Division Method

Prime factorization is expressing a number as a product of its prime factors.
For example, factors of 6 are 1, 2, 3, 6
6 = 2 × 3
So, the prime factors of 6 are 2 and 3.

The upside-down division got its name because the division symbol is flipped upside down.

• STEP 1: By using divisibility rules, we find out the smallest exact prime divisor (factor) of the given number. Here, 18 is an even number. So it is divisible by 2. In other words, 2 divides 18 with no remainder. Therefore, 2 is the smallest prime factor of 18.
• STEP 2: We divide the given number by its smallest factor other than 1 (prime factor), 18 ÷ 2 = 9
• STEP 3: We then find the prime factors of the obtained quotient. Repeat Step 1 and Step 2 till we get a prime number as the quotient. Here, 9 is the quotient, 9 ÷ 3= 3
• 3 is the quotient, so we stop the process here. Therefore, 18 = 2 × 3 × 3

Prime Factorization by Factor Tree Method

First, we identify the two factors that give 18. 18 is the root of this factor tree.
18 = × 6
Here, 6 is a composite number. So it can be further factorized.
6 = 3 × 2
We continue this process until we are left with only prime numbers, i.e., till we cannot further factor the obtained numbers.
We then circle all the prime numbers in the factor tree. Basically, we branch out 18 into its prime factors.

So, the prime factorization of 18 is 18= 2 × 3 × 3.

A factor tree is not unique for a given number. Instead of expressing 18 as 2 × 9, we can express 18 as 3 × 6. Here is a simple activity to try on your own. Instead of 2 × 9, if I had used 3 × 6, do you think we would get the same factors?
Can you draw the factor tree with 3 and 6 as the branches?

Explore factors using illustrations and interactive examples

• Factors of 17: The factors of 17 are 1 and 17.
• Factors of 12: The factors of 12 are 1, 2, 3, 4, 6, and 12.
• Factors of 19:  The factors of 19 are 1 and 19.
• Factors of 180: The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
• Factors of 13: The factors of 13 are 1 and 13.

Factor pairs are the two numbers that, when multiplied, give the number 18.

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

Therefore, pair factors of 18 are (1,18), (2,9), and (3,6). A factor rainbow helps you find all of the factors. It is called a rainbow because all of the factor pairs connect to make a rainbow! Making a factor rainbow is quite easy. 

Let’s try one:
Find all of the factors for the number 18.

• Step I: Start with 1 and the number itself.
• Step II: Count up by ones to see if you can multiply two numbers together to get your target number.
• Step III: Stop when you can’t get any more numbers in between.
• Step IV: Connect the factor pairs.

Important Notes:

• Factors of a number are the numbers that divide the given number exactly without any remainder.
• 18 is a composite number as it has more factors other than 1 and itself.
• Pair factors of 18 are (1,18), (2,9), and (3,6).
• 1 is a factor of every number.
• The factor of a number is always less than or equal to the given number.
• Prime factorization is expressing the number as a product of its prime factors.

• 90 × 0.2= 18. Can we conclude (90, 0.2) as a factor pair of 18?
• Is the number of factors of a given number finite?
• Can the factor of a number be greater than the number itself?