Factors of 18

What are the Factors of 18?

Factors of 18 is the product of such numbers which completely divide the given number 18. Factors of a given number have two values; they can be either positive or negative numbers. By multiplying the factors of a number we get the original number. For example 1, 2, 3, 4, 6, 12 are the factors of 12. Hence we have 4 x 3 = 12 or 6 x 2 = 12 as the pair factors of 12. In this article, we will study the factors of 18, what are the factors of 18, what is the prime factorization of 18, factor tree of 18, all factors of 18 and examples. Factor pairs of the number 18 are the pairs of the whole numbers which could be either positive or negative but not a fraction or decimal number. Factorisation is the common method to find the factors of 18. 

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Factors of 18 Definition

The factors of a number are defined as the numbers which give the original number on multiplying the two factors.The factors can be either positive or negative integers. Factors of 18 are all the integers that can evenly divide the given number 18.

Now let us study how to calculate all factors of 18.

What are the Factors of 18?

According to the definition of factors of 18, we know that factors of 18 are all the positive or negative integers which divide the number 18 completely. So let us simply divide the number 18 by every number which completely divides 18 in ascending order till 18.

18 ÷ 1 = 18

18 ÷ 2 = 9

18 ÷ 3 = 6

18 ÷ 4 = not divides completely

18 ÷ 5 = not divides completely

18 ÷ 6 = 3

18 ÷ 7 = not divides completely

18 ÷ 8 =  not divides completely

18 ÷ 9 = 2

18 ÷18 = 1

So all factors of 18: 1, 2, 3, 6, 9, and 18.

We know that factors also include negative integers hence we can also have, 

list of negative factors of 18: -1, -2, -3, -6, -9 and -18.

All Factors of 18 Can be Listed as Follows.

Positive Factors of 18

1, 2, 3, 6, 9 and 18

Negative Factors of 18

-1, -2, -3, -6, -9 and -18.


Hence 18 have total 6 positive factors and 6 negative factors.

All Factor Pairs of 18

All Factor Pairs of 18 are combinations of two factors that when multiplied together give 18.

List of all the positive pair factors of 18

1 x 18 = 18; pair factors are(1, 18)

3 x 6 = 18; pair factors are(3, 6)

2 x 9 = 18; pair factors are(2, 9)

So (1, 18), (3, 6) and ( 2, 9), are the positive pair factors of 18

As we know that Factors of 18 include negative integers too. 

List of all the negative pair factors of 18:

-1 x -18 = 18

-3 x -6 = 18

-2 x -9 = 18

So (-1, -18), (-3, -6) and ( -2, -9) are the negative pair factors of 18

Now we will study what is the prime factorization of 18.

What is the Prime Factorization of 18

According to the prime factor definition, we know that the prime factor of a number is the product of all the factors that are prime that is a number that divides by itself and only one. Hence we can list the prime factors from the list of factors of 18.

Or the other way to find the prime factorization of 18 is by prime factorization or by factor tree of 18.

Now let us study prime factors of 18 by division method.

Prime Factors of 18 by Division Method

To calculate the prime factors of 18 by division method, first, take the least prime number that is 2. Divide it by 2 until it is completely divisible by 2. If at a point it is not divisible by 2 take the next least prime number that is 3. Perform the same steps and move forward, till we get 1, as the quotient. Here is the stepwise method to calculate the prime factors of 18

Step 1: Divide 18 with 2

18 ÷ 2 = 9

Step 2: Divide 9 with 2

9 ÷ 2 = not divisible

Step 4: So take another prime number 3 divide with 3

9 ÷ 3 = 3

Step 5: Now again divide 3 by 3

3 ÷ 3 = 1 

We get the quotient 1.

From the above steps, we get a prime factor of 18 as 2 x 3 x 3 = 2 x 32

Here is the factor tree of 18.

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Factor tree of 18

Solved Examples

Example 1: Find the prime factors of 180.

Solution: 

  180 = 2 x 90

= 2 x 2 x 45

= 2 x 2 x 5 x 9

= 2 x 2 x 5 x 3 x 3

Example 2: Find the factors for 48

Solution:

48 ÷ 1 = 48

48 ÷ 2 = 24

48 ÷ 3 = 16

48 ÷ 4 = 12

48 ÷ 5 = not divides completely

48 ÷ 6 = 8

48 ÷ 7 = not divides completely

48 ÷ 8 = 6

48 ÷ 9 = not divide completely 

48 ÷12 = 4

48 ÷ 16 = 3

48 ÷ 24 =12

48 ÷ 48 = 1

So all factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

list of negative factors of 48: -1, -2, -3, -4, -6, -8, -12, -16, -24 and -48.

Hence 48 have total 10 positive factors and 10 negative factors.

Facts:

  • A factor of any number divides the given number exactly.

  • 1 is a common factor.

  • Each factor of a number is less than or equal to the original number.

  • The number itself is the greatest factor of itself.

FAQ (Frequently Asked Questions)

1. What is Factor Tree?

Answer: Factoring tree means splitting a large number into its prime factors. Place the number you wish to factor at the top of the expression, and divide it in steps by least prime number which are the factors of the number. Each time you divide a number, place the number's two factors below. Continue dividing until all numbers have been reduced to their prime numbers which are factors. You can  divide by composite factors to create a factor tree. When you divide by a composite factor, you then split up the composite factor into its prime factors. 

For example,Factor tree for 1260

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2. What are the Multiples of a Number?

Answer: Multiples are the number which divide the number completely without the remainder. Multiples are the product of a given number with an integer. For example we can say that multiples of 8 are the numbers obtained by the product of 8 with the natural numbers like 1, 2, 3, 4,....so on. Some of the multiples of 8 are 8, 16, 24, 32, 40, 48 and so on….It is impossible to list all multiples of 8, since there are an infinite number of natural numbers. In this article let us study all the multiples of 8 and how to determine multiples of 8.