Factor Calculator

Factors of 1098

The factors of 1098 are 1, 2, 3, 6, 9, 18, 61, 122, 183, 366, 549, and 1098. In total, 1098 has 12 factors. Its prime factorization is 2 × 3² × 61, and the sum of all its factors is 2418.

All factors of 1098

Here are all 12 factors of 1098, listed from smallest to largest.

1236918611221833665491098

Factor pairs of 1098

These 6 pairs of whole numbers each multiply to give 1098.

1 × 1098 = 1098
2 × 549 = 1098
3 × 366 = 1098
6 × 183 = 1098
9 × 122 = 1098
18 × 61 = 1098

Prime factorization of 1098

Dividing 1098 by the smallest prime at each step gives its prime factorization:

1098 ÷ 2 = 549
549 ÷ 3 = 183
183 ÷ 3 = 61
61 ÷ 61 = 1
Result: 1098 = 2 × 3 × 3 × 61 = 2 × 3² × 61

The distinct prime factors of 1098 are 2, 3, 61. To factorize any other number, use the prime factorization calculator.

Factor tree of 1098

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

Factor tree of 1098109825493183361
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 1098

Number of factors12
Sum of factors2418
Sum of proper factors1320
Prime factorization2 × 3² × 61
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 1098 interesting

  • 1098 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.
  • 1098 is an abundant number: its proper factors sum to 1320, which is 222 more than 1098 itself.
  • 1098 has 3 distinct prime factors (2, 3, 61), which is why it has so many divisors.

How to find the factors of 1098 yourself

Divide 1098 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 √109833.14, because every factor above that pairs with one below it.

1098 ÷ 1 = 1098
1098 ÷ 2 = 549
1098 ÷ 3 = 366
1098 ÷ 6 = 183
1098 ÷ 9 = 122
1098 ÷ 18 = 61

Reading both columns gives every factor: 1, 2, 3, 6, 9, 18, 61, 122, 183, 366, 549, 1098. The factor calculator does this automatically for any number.

Frequently asked questions about 1098

What are the factors of 1098?

The factors of 1098 are 1, 2, 3, 6, 9, 18, 61, 122, 183, 366, 549, and 1098. That is 12 factors in total, counting both 1 and 1098.

Is 1098 a prime number?

No, 1098 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 1098 is also divisible by 2.

What is the prime factorization of 1098?

The prime factorization of 1098 is 2 × 3² × 61. Written out in full: 2 × 3 × 3 × 61 = 1098. Its distinct prime factors are 2, 3, 61.

What two numbers multiply to give 1098?

There are 6 pairs of whole numbers that multiply to 1098: 1 × 1098, 2 × 549, 3 × 366, 6 × 183, 9 × 122, 18 × 61.

What is the sum of the factors of 1098?

Adding all the factors of 1098 together gives 2418. Excluding 1098 itself, the proper factors sum to 1320.

Is 1098 a perfect square?

No, 1098 is not a perfect square. There is no whole number that multiplies by itself to give 1098. The nearest perfect squares are 1089 and 1156.

What is the largest factor of 1098 other than itself?

The largest factor of 1098 apart from 1098 itself is 549, since 1098 ÷ 549 = 2.

How many factors does 1098 have?

1098 has 12 factors: 1, 2, 3, 6, 9, 18, 61, 122, 183, 366, 549, and 1098. You can verify this from the prime factorization 2 × 3² × 61: add 1 to each exponent and multiply, giving 2 × 3 × 2 = 12.

Explore more

Try another number in the factor calculator, break 1098 down further with the prime factorization calculator, or compare 1098 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.