Factors Of 18 | With Easy Division and Prime Factorization

Factors Of 18

When multiplied together in pairs, factors of 18 give the original number 18. Basically, a factor is only a number that divides the original number completely. 

Multiplication of 18 results in the original number being the pair factor. In contrast to decimals and fractions, the pair factor of 18 can be both positive and negative.

Hence, (1, 18) or (-1, -18) can be written as the pair factor of 18. By multiplying two negative numbers, such as -1 and -18, we will get the original number 18. 

I will explain the prime factorization method and the factors of 18 using many examples of solved examples using the prime factorization method.

What are the Factors of 18?

A factor of 18 is any number that divides 18 completely without leaving a remainder. Basically, the multiplied numbers that result in 18 are the factors of 18.

Because 18 is an even number, it has more factors other than 1 and 18. Therefore, the factors of 18 are 1, 2, 3, 6, 9, and 18.

Factors of 18: 1, 2, 3, 6, 9, and 18.

Prime Factorization of 18: 2 × 3 × 3 or 2 × 3².

What are the Factors Of -18?

Factors of -24 are -1, -2, -3, -6, -9 and -18.

We can get -18 by having (-1, 18), (-2,9), and (-3, 6) as a pair of factors. Similarly, we can also get -18 by having (1, -18), (2, -9), and (3, -6) as a pair of factors.

Pair Factors of 18

A pair factor of 18 results from multiplying together two numbers and resulting in 18. As discussed above, pair factor 18 can be positive or negative. Here are the positive and negative pairs for 18:

Positive Pair Factors of 18:

Negative Pair Factor of 18:

Consequently, the positive pair factors of 18 are (1, 18), (2, 9), and (3, 6). Furthermore, the negative pair factors of 18 are (-1, -18), (-2, -9), and (-3, -6).

Factors of 18 by Division Method

In the division method, 18 is divided by different integers to find its factors. Integers that divide 18 exactly and leave a zero remainder are factors of 18. Now that we’ve divided 18 by 1 let’s move on to the next integer.

• 18/1 = 18  (Factor is 1 and Remainder = 0)
• 18/2 = 9    (Factor is 2 and Remainder = 0)
• 18/3 = 6    (Factor is 3 and Remainder = 0)
• 18/6 = 3    (Factor is 6 and Remainder = 0)
• 18/9 = 2    (Factor is 9 and Remainder = 0)
• 18/18 = 1   (Factor is 18 and Remainder is 0)

A remainder is left over when 18 is divided by any number except 1, 2, 3, 6, 9, and 18. This means that the factors of 18 are 1, 2, 3, 6, 9, and 18.

Prime Factorization of 18

In mathematics, the number 18 is a composite number. We can now find the prime factors of this number.

• Firstly, divide 18 by the smallest prime number, i.e., 2.

18 ÷ 2 = 9

• Determine if you can further divide 9 by 2.

9 ÷ 2 = 4.5

          The result is a fractional value. Factors must be whole numbers.

Our next prime number is 3, so we will go to 3.

• Divide 9 by 3 now.

9 ÷ 3 = 3

• Divide again 3 by 3.

3 ÷ 3 = 1

• In addition, we received 1 at the end, which prevents us from dividing. In other words, 18 has the prime factors 2 × 3 × 3 or 2 × 3², where 2 and 3 are both prime numbers.

Examples

Example 1:

What are the common factors of 18 and 56?

Solution:

One, two, three, six, nine, and 18 are the factors of 18.

Factors of 57 = 1, 3, 19, and 57.

18 and 57 have a common factor of 1.

Example 2:

What are the common factors of 24 and 19?

Solution:

The factors of 24 are 1, 2, 3, 6, 8, 12, and 24.

There are two factors of 19: 1 and 19.

Because 19 is a prime number, 24 and 19 have 1 in common.

Example 3:

Find the common factor between 18 and 25.

Solution:

18 has the following factors: 1, 2, 3, 6, 9, and 18.

Factors of 25 are 1, 5, and 25.

In other words, 18 and 25 have a common factor 1.

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