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Factors of 198

Factors of 198 are the list of integers that we can split evenly into 198. There are 12 factors of 198, of which the following are its prime factors 2, 3, 11. The Prime Factorization of 198 is 21 × 32 × 111.

  • All Factors of 198: 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99 and 198
  • Prime Factors of 198: 2, 3, 11
  • Prime Factorization of 198: 21 × 32 × 111
  • Sum of Factors of 198: 468
1. What Are the Factors of 198?
2. Factors of 198 by Prime Factorization
3. Factors of 198 in Pairs
4. FAQs on Factors of 198
Factors of 198

What are Factors of 198?

Factors of 198 are pairs of those numbers whose products result in 198. These factors are either prime numbers or composite numbers.

How to Find the Factors of 198?

To find the factors of 198, we will have to find the list of numbers that would divide 198 without leaving any remainder.

  • 198/66 = 3; therefore, 66 is a factor of 198 and 3 is also a factor of 198.
  • 198/99 = 2; therefore, 99 is a factor of 198 and 2 is also a factor of 198.
Similarly we can find other factors. Hence, the factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198.

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Factors of 198 by Prime Factorization

The number 198 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 198. The first step is to divide the number 198 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 198 ÷ 2 = 99

Further dividing 99 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 99 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 198 can be written as 21 × 32 × 111 where 2, 3, 11 are prime.

 

Factors of 198 in Pairs

Pair factors of 198 are the pairs of numbers that when multiplied give the product 198. The factors of 198 in pairs are:

  • 1 × 198 = (1, 198)
  • 2 × 99 = (2, 99)
  • 3 × 66 = (3, 66)
  • 6 × 33 = (6, 33)
  • 9 × 22 = (9, 22)
  • 11 × 18 = (11, 18)

Negative pair factors of 198 are:

  • -1 × -198 = (-1, -198)
  • -2 × -99 = (-2, -99)
  • -3 × -66 = (-3, -66)
  • -6 × -33 = (-6, -33)
  • -9 × -22 = (-9, -22)
  • -11 × -18 = (-11, -18)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 198 Solved Examples

  1. Example 1: How many factors are there for 198?

    Solution:

    The factors of 198 are too many, therefore if we can find the prime factorization of 198, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

    Prime Factorization of 198 = 21 × 32 × 111
    Therefore, the total number of factors are (1 + 1) × (2 + 1) × (1 + 1) = 2 × 3 × 2 = 12

  2. Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Factor (GCF) of 198 and 187.

    Solution:

    The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198 and factors of 187 are 1, 11, 17, 187.

    Therefore, the Lowest Common Multiple (LCM) of 198 and 187 is 3366 and Greatest Common Factor (GCF) of 198 and 187 is 11.

  3. Example 3: Find if 2, 3, 9, 11, 66, 171 and 198 are factors of 198.

    Solution:

    When we divide 198 by 171 it leaves a remainder. Therefore, the number 171 is not a factor of 198. All numbers except 171 are factors of 198.

  4. Example 4: Find the product of all the prime factors of 198.

    Solution:

    Since, the prime factors of 198 are 2, 3, 11. Therefore, the product of prime factors = 2 × 3 × 11 = 66.

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FAQs on Factors of 198

What are the Factors of 198?

The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198 and its negative factors are -1, -2, -3, -6, -9, -11, -18, -22, -33, -66, -99, -198.

What is the Sum of all Factors of 198?

Sum of all factors of 198 = (21 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (111 + 1 - 1)/(11 - 1) = 468

What are the Pair Factors of 198?

The pair factors of 198 are (1, 198), (2, 99), (3, 66), (6, 33), (9, 22), (11, 18).

What is the Greatest Common Factor of 198 and 35?

The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198 and the factors of 35 are 1, 5, 7, 35. 198 and 35 have only one common factor which is 1. This implies that 198 and 35 are co-prime.

Hence, the Greatest Common Factor (GCF) of 198 and 35 is 1.

How Many Factors of 75 are also common to the Factors of 198?

Since, the factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198 and the factors of 75 are 1, 3, 5, 15, 25, 75.
Hence, [1, 3] are the common factors of 198 and 75.

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