Factor Calculator

Factors of 198

The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, and 198. In total, 198 has 12 factors. Its prime factorization is 2 × 3² × 11, and the sum of all its factors is 468.

All factors of 198

Here are all 12 factors of 198, listed from smallest to largest.

12369111822336699198

Factor pairs of 198

These 6 pairs of whole numbers each multiply to give 198.

1 × 198 = 198
2 × 99 = 198
3 × 66 = 198
6 × 33 = 198
9 × 22 = 198
11 × 18 = 198

Prime factorization of 198

Dividing 198 by the smallest prime at each step gives its prime factorization:

198 ÷ 2 = 99
99 ÷ 3 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1
Result: 198 = 2 × 3 × 3 × 11 = 2 × 3² × 11

The distinct prime factors of 198 are 2, 3, 11. To factorize any other number, use the prime factorization calculator.

Factor tree of 198

A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.

Factor tree of 198198299333311
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 198

Number of factors12
Sum of factors468
Sum of proper factors270
Prime factorization2 × 3² × 11
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 198 interesting

  • 198 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 6 different ways.
  • 198 is an abundant number: its proper factors sum to 270, which is 72 more than 198 itself.
  • 198 has 3 distinct prime factors (2, 3, 11), which is why it has so many divisors.

How to find the factors of 198 yourself

Divide 198 by each whole number starting from 1. Whenever the division leaves no remainder, both the divisor and the quotient are factors. You only need to test up to √198 ≈ 14.07, because every factor above that pairs with one below it.

198 ÷ 1 = 198 ✓
198 ÷ 2 = 99 ✓
198 ÷ 3 = 66 ✓
198 ÷ 6 = 33 ✓
198 ÷ 9 = 22 ✓
198 ÷ 11 = 18 ✓

Reading both columns gives every factor: 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198. The factor calculator does this automatically for any number.

Numbers mathematically connected to 198.

Frequently asked questions about 198

What are the factors of 198?

The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, and 198. That is 12 factors in total, counting both 1 and 198.

Is 198 a prime number?

No, 198 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 198 is also divisible by 2.

What is the prime factorization of 198?

The prime factorization of 198 is 2 × 3² × 11. Written out in full: 2 × 3 × 3 × 11 = 198. Its distinct prime factors are 2, 3, 11.

What two numbers multiply to give 198?

There are 6 pairs of whole numbers that multiply to 198: 1 × 198, 2 × 99, 3 × 66, 6 × 33, 9 × 22, 11 × 18.

What is the sum of the factors of 198?

Adding all the factors of 198 together gives 468. Excluding 198 itself, the proper factors sum to 270.

Is 198 a perfect square?

No, 198 is not a perfect square. There is no whole number that multiplies by itself to give 198. The nearest perfect squares are 196 and 225.

What is the largest factor of 198 other than itself?

The largest factor of 198 apart from 198 itself is 99, since 198 ÷ 99 = 2.

How many factors does 198 have?

198 has 12 factors: 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, and 198. You can verify this from the prime factorization 2 × 3² × 11: add 1 to each exponent and multiply, giving 2 × 3 × 2 = 12.

Explore more

Try another number in the factor calculator, break 198 down further with the prime factorization calculator, or compare 198 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.