Factors of 198

The numbers that divide 198 evenly are known as factors of 198. A factor of 198 is a number that divides the number without remainder. The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, and 198.

Negative factors of 198: -1, -2, -3, -6, -9, -11, -18, -22, -33, -66, -99, -198.

Prime factors of 198: 2, 3, and 11.

Prime factorization of 198: 2 × 3² × 11.

The sum of factors of 198: 1 + 2 + 3 + 6 + 9 + 11 + 18 + 22 + 33 + 66 + 99 + 198 = 468

Factors can be found using different methods. Mentioned below are some commonly used methods:

1. Finding factors using multiplication
2. Finding factors using the division method
3. Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 198. Identifying the numbers which are multiplied to get the number 198 is the multiplication method.

Step 1: Multiply 198 by 1, 198 × 1 = 198.

Step 2: Check for other numbers that give 198 after multiplying    

 2 × 99 = 198     

3 × 66 = 198    

 6 × 33 = 198     

9 × 22 = 198     

11 × 18 = 198

Therefore, the positive factor pairs of 198 are: (1, 198), (2, 99), (3, 66), (6, 33), (9, 22), (11, 18). For every positive factor, there is a negative factor.

Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -

Step 1: Divide 198 by 1, 198 ÷ 1 = 198.

Step 2: Continue dividing 198 by the numbers until the remainder becomes 0.

198 ÷ 1 = 198

198 ÷ 2 = 99

198 ÷ 3 = 66

198 ÷ 6 = 33

198 ÷ 9 = 22

198 ÷ 11 = 18

Therefore, the factors of 198 are: 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198.

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
• Using a factor tree

Using Prime Factorization: In this process, prime factors of 198 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

198 ÷ 2 = 99

99 ÷ 3 = 33

33 ÷ 3 = 11

11 ÷ 11 = 1

The prime factors of 198 are 2, 3, and 11. The prime factorization of 198 is: 2 × 3² × 11.

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 198 is divided by 2 to get 99.

Step 2: Now divide 99 by 3 to get 33.

Step 3: Then divide 33 by 3 to get 11. Here, 11 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 198 is: 2 × 3² × 11.

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

• Positive factor pairs of 198: (1, 198), (2, 99), (3, 66), (6, 33), (9, 22), and (11, 18).
• Negative factor pairs of 198: (-1, -198), (-2, -99), (-3, -66), (-6, -33), (-9, -22), and (-11, -18).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 198 are 1, 2, 3, 6, etc.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 11 are prime factors of 198.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 198 are (1, 198), (2, 99), etc.

• Prime factorization: Expressing a number as a product of its prime factors. For example, 198 = 2 × 3² × 11.

• Multiple: A number that can be divided by another number without a remainder. For example, 198 is a multiple of 9.