1. Steps to find factors of 108 using Division Method

Example: Find factors of 108

  • Divide 108 by 1: 108 ÷ 1 : Remainder = 0
  • Divide 108 by 2: 108 ÷ 2 : Remainder = 0
  • Divide 108 by 3: 108 ÷ 3 : Remainder = 0
  • Divide 108 by 4: 108 ÷ 4 : Remainder = 0
  • Divide 108 by 6: 108 ÷ 6 : Remainder = 0
  • Divide 108 by 9: 108 ÷ 9 : Remainder = 0
  • Divide 108 by 12: 108 ÷ 12 : Remainder = 0
  • Divide 108 by 18: 108 ÷ 18 : Remainder = 0
  • Divide 108 by 27: 108 ÷ 27 : Remainder = 0
  • Divide 108 by 36: 108 ÷ 36 : Remainder = 0
  • Divide 108 by 54: 108 ÷ 54 : Remainder = 0
  • Divide 108 by 108: 108 ÷ 108 : Remainder = 0

Hence, Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108

2. Steps to find factors of 108 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 108 using the division method, follow these steps:

  • Step 1. Start dividing 108 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 108, which is 2. Divide 108 by 2 to obtain the quotient (54).
    108 ÷ 2 = 54
  • Step 3. Repeat step 1 with the obtained quotient (54).
    54 ÷ 2 = 27
    27 ÷ 3 = 9
    9 ÷ 3 = 3
    3 ÷ 3 = 1

So, the prime factorization of 108 is, 108 = 2 x 2 x 3 x 3 x 3.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 108 as shown below:

So, the prime factorization of 108 is, 108 = 2 x 2 x 3 x 3 x 3.

3. Find factors of 108 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 108 would be the two numbers which, when multiplied, give 108 as the result.

The following table represents the calculation of factors of 108 in pairs:

Factor Pair Pair Factorization
1 and 108 1 x 108 = 108
2 and 54 2 x 54 = 108
3 and 36 3 x 36 = 108
4 and 27 4 x 27 = 108
6 and 18 6 x 18 = 108
9 and 12 9 x 12 = 108

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 108. They are called negative pair factors.

Hence, the negative pairs of 108 would be ( -1 , -108 ) , ( -2 , -54 ) , ( -3 , -36 ) , ( -4 , -27 ) , ( -6 , -18 ) and ( -9 , -12 ) .

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 108 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 108.
  • Every number is a factor of zero (0), since 108 x 0 = 0.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 are exact divisors of 108.
  • Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. Each factor divides 108 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 are all less than or equal to 108.

Frequently Asked Questions

  • Which is the smallest prime factor of 108?

    Smallest prime factor of 108 is 2.

  • Is 108 a perfect square?

    No 108 is not a perfect square.

  • What are five multiples of 108?

    First five multiples of 108 are 216, 324, 432, 540, 648.

  • What is prime factorization of 108?

    Prime factorization of 108 is 2 x 2 x 3 x 3 x 3.

  • What are factors of 108?

    Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.

  • How do you find factors of a negative number? ( eg. -108 )?

    Factors of -108 are -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, -108.

  • Is 108 a whole number?

    Yes 108 is a whole number.

  • Which is greatest factor of 108?

    The greatest factor of 108 is 54.

  • What are the prime factors of 108?

    The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.
    Prime factors of 108 are 2, 2, 3, 3, 3.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 108. Can you help her?

Prime factors of 108 are 2, 2, 3, 3, 3.
Hence, the product of prime factors of 6.

Can you help Rubel to find out the product of the even factors of 108?

Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.
Even factors of 108 are 2, 4, 6, 12, 18, 36, 54, 108.
Hence, product of even factors of 108 is; 2 x 4 x 6 x 12 x 18 x 36 x 54 x 108 = 2176782336.

Joy wants to calculate mean of all the factors of 108. Help him in finding the mean of 108.

Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 108 is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 108 = 280.
Hence, the mean of factors of 108 is 280 ÷ 12 = 23.33.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 108? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.
Negative factors are -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, -108.

How many factors are there for 108?

Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.
So there are in total 12 factors.

Joey wants to write all the prime factors of 108 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 108 are 2, 2, 3, 3, 3.
So in exponential form it can be written as 22 x 33.

Kevin has been asked to write 11 factor(s) of 108. Can you predict the answer?

11 factor(s) of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54.