Factor Calculator

Factors of 306

The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, and 306. In total, 306 has 12 factors. Its prime factorization is 2 × 3² × 17, and the sum of all its factors is 702.

All factors of 306

Here are all 12 factors of 306, listed from smallest to largest.

1236917183451102153306

Factor pairs of 306

These 6 pairs of whole numbers each multiply to give 306.

1 × 306 = 306
2 × 153 = 306
3 × 102 = 306
6 × 51 = 306
9 × 34 = 306
17 × 18 = 306

Prime factorization of 306

Dividing 306 by the smallest prime at each step gives its prime factorization:

306 ÷ 2 = 153
153 ÷ 3 = 51
51 ÷ 3 = 17
17 ÷ 17 = 1
Result: 306 = 2 × 3 × 3 × 17 = 2 × 3² × 17

The distinct prime factors of 306 are 2, 3, 17. To factorize any other number, use the prime factorization calculator.

Factor tree of 306

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

Factor tree of 3063062153351317
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 306

Number of factors12
Sum of factors702
Sum of proper factors396
Prime factorization2 × 3² × 17
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 306 interesting

  • 306 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.
  • 306 is an abundant number: its proper factors sum to 396, which is 90 more than 306 itself.
  • 306 has 3 distinct prime factors (2, 3, 17), which is why it has so many divisors.

How to find the factors of 306 yourself

Divide 306 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 √306 ≈ 17.49, because every factor above that pairs with one below it.

306 ÷ 1 = 306 ✓
306 ÷ 2 = 153 ✓
306 ÷ 3 = 102 ✓
306 ÷ 6 = 51 ✓
306 ÷ 9 = 34 ✓
306 ÷ 17 = 18 ✓

Reading both columns gives every factor: 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306. The factor calculator does this automatically for any number.

Numbers mathematically connected to 306.

Frequently asked questions about 306

What are the factors of 306?

The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, and 306. That is 12 factors in total, counting both 1 and 306.

Is 306 a prime number?

No, 306 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 306 is also divisible by 2.

What is the prime factorization of 306?

The prime factorization of 306 is 2 × 3² × 17. Written out in full: 2 × 3 × 3 × 17 = 306. Its distinct prime factors are 2, 3, 17.

What two numbers multiply to give 306?

There are 6 pairs of whole numbers that multiply to 306: 1 × 306, 2 × 153, 3 × 102, 6 × 51, 9 × 34, 17 × 18.

What is the sum of the factors of 306?

Adding all the factors of 306 together gives 702. Excluding 306 itself, the proper factors sum to 396.

Is 306 a perfect square?

No, 306 is not a perfect square. There is no whole number that multiplies by itself to give 306. The nearest perfect squares are 289 and 324.

What is the largest factor of 306 other than itself?

The largest factor of 306 apart from 306 itself is 153, since 306 ÷ 153 = 2.

How many factors does 306 have?

306 has 12 factors: 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, and 306. You can verify this from the prime factorization 2 × 3² × 17: add 1 to each exponent and multiply, giving 2 × 3 × 2 = 12.

Explore more

Try another number in the factor calculator, break 306 down further with the prime factorization calculator, or compare 306 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.