Factor Calculator

Factors of 289

The factors of 289 are 1, 17, and 289. In total, 289 has 3 factors. Its prime factorization is 17², and the sum of all its factors is 307. 289 is also a perfect square, equal to 17 × 17.

All factors of 289

Here are all 3 factors of 289, listed from smallest to largest.

117289

Factor pairs of 289

These 2 pairs of whole numbers each multiply to give 289.

1 × 289 = 289
17 × 17 = 289

Notice the pair (17, 17) — because 289 is a perfect square, this pair uses the same number twice.

Prime factorization of 289

Dividing 289 by the smallest prime at each step gives its prime factorization:

289 ÷ 17 = 17
17 ÷ 17 = 1
Result: 289 = 17 × 17 = 17²

The distinct prime factors of 289 are 17. To factorize any other number, use the prime factorization calculator.

Factor tree of 289

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

Factor tree of 2892891717
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 289

Number of factors3
Sum of factors307
Sum of proper factors18
Prime factorization17²
Prime or composite?Composite
Even or odd?Odd
Perfect square?Yes (17²)
Perfect cube?No
ClassificationDeficient

What makes 289 interesting

  • 289 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 2 different ways.
  • 289 is a perfect square: 17 × 17 = 289. This is why it has an odd number of factors (3) — the pair (17, 17) counts only once.
  • 289 is a deficient number: its proper factors sum to 18, which is 271 less than 289 itself.
  • 289 is a prime power: it is 17 raised to the power of 2. All of its factors are powers of 17.

How to find the factors of 289 yourself

Divide 289 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 √289 ≈ 17.00, because every factor above that pairs with one below it.

289 ÷ 1 = 289 ✓
289 ÷ 17 = 17 ✓

Reading both columns gives every factor: 1, 17, 289. The factor calculator does this automatically for any number.

Numbers mathematically connected to 289.

Frequently asked questions about 289

What are the factors of 289?

The factors of 289 are 1, 17, and 289. That is 3 factors in total, counting both 1 and 289.

Is 289 a prime number?

No, 289 is not prime — it is a composite number with 3 factors. A prime number has exactly two factors, but 289 is also divisible by 17.

What is the prime factorization of 289?

The prime factorization of 289 is 17². Written out in full: 17 × 17 = 289. Its distinct prime factors are 17.

What two numbers multiply to give 289?

There are 2 pairs of whole numbers that multiply to 289: 1 × 289, 17 × 17.

What is the sum of the factors of 289?

Adding all the factors of 289 together gives 307. Excluding 289 itself, the proper factors sum to 18.

Is 289 a perfect square?

Yes, 289 is a perfect square. It equals 17 × 17. Perfect squares always have an odd number of factors — 289 has 3.

What is the largest factor of 289 other than itself?

The largest factor of 289 apart from 289 itself is 17, since 289 ÷ 17 = 17.

How many factors does 289 have?

289 has 3 factors: 1, 17, and 289. You can verify this from the prime factorization 17²: add 1 to each exponent and multiply, giving 3 = 3.

Explore more

Try another number in the factor calculator, break 289 down further with the prime factorization calculator, or compare 289 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.