Is 289 a prime number? What are the divisors of 289?

Is 289 a prime number?

It is possible to find out using mathematical methods whether a given integer is a prime number or not.

For 289, the answer is: No, 289 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 289) is as follows: 1, 17, 289.

To be 289 a prime number, it would have been required that 289 has only two divisors, i.e., itself and 1.

As a consequence:

  • 289 is a multiple of 1
  • 289 is a multiple of 17

To be 289 a prime number, it would have been required that 289 has only two divisors, i.e., itself and 1.

However, 289 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 289 = 17 x 17, where 17 is a prime number.

Is 289 a deficient number?

Yes, 289 is a deficient number, that is to say 289 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 289 without 289 itself (that is 1 + 17 = 18).

Parity of 289

289 is an odd number, because it is not evenly divisible by 2.

Is 289 a perfect square number?

A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 289 is 17.

Therefore, the square root of 289 is an integer, and as a consequence 289 is a perfect square.

As a consequence, 17 is the square root of 289.

What is the square number of 289?

The square of a number (here 289) is the result of the product of this number (289) by itself (i.e., 289 × 289); the square of 289 is sometimes called "raising 289 to the power 2", or "289 squared".

The square of 289 is 83 521 because 289 × 289 = 2892 = 83 521.

As a consequence, 289 is the square root of 83 521.

Number of digits of 289

289 is a number with 3 digits.

What are the multiples of 289?

The multiples of 289 are all integers evenly divisible by 289, that is all numbers such that the remainder of the division by 289 is zero. There are infinitely many multiples of 289. The smallest multiples of 289 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 289 too, since 0 × 289 = 0
  • 289: indeed, 289 is a multiple of itself, since 289 is evenly divisible by 289 (we have 289 / 289 = 1, so the remainder of this division is indeed zero)
  • 578: indeed, 578 = 289 × 2
  • 867: indeed, 867 = 289 × 3
  • 1 156: indeed, 1 156 = 289 × 4
  • 1 445: indeed, 1 445 = 289 × 5
  • etc.

How to determine whether an integer is a prime number?

To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 289). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is 17). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.

More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.

Numbers near 289

  • Preceding numbers: …287, 288
  • Following numbers: 290, 291

Nearest numbers from 289

  • Preceding prime number: 283
  • Following prime number: 293
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