Is 209 a prime number? What are the divisors of 209?

Is 209 a prime number?

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

For 209, the answer is: No, 209 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 209) is as follows: 1, 11, 19, 209.

To be 209 a prime number, it would have been required that 209 has only two divisors, i.e., itself and 1.

As a consequence:

  • 209 is a multiple of 1
  • 209 is a multiple of 11
  • 209 is a multiple of 19

To be 209 a prime number, it would have been required that 209 has only two divisors, i.e., itself and 1.

However, 209 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 209 = 11 x 19, where 11 and 19 are both prime numbers.

Is 209 a deficient number?

Yes, 209 is a deficient number, that is to say 209 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 209 without 209 itself (that is 1 + 11 + 19 = 31).

Parity of 209

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

Is 209 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 209 is about 14.457.

Thus, the square root of 209 is not an integer, and therefore 209 is not a square number.

What is the square number of 209?

The square of a number (here 209) is the result of the product of this number (209) by itself (i.e., 209 × 209); the square of 209 is sometimes called "raising 209 to the power 2", or "209 squared".

The square of 209 is 43 681 because 209 × 209 = 2092 = 43 681.

As a consequence, 209 is the square root of 43 681.

Number of digits of 209

209 is a number with 3 digits.

What are the multiples of 209?

The multiples of 209 are all integers evenly divisible by 209, that is all numbers such that the remainder of the division by 209 is zero. There are infinitely many multiples of 209. The smallest multiples of 209 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 209 too, since 0 × 209 = 0
  • 209: indeed, 209 is a multiple of itself, since 209 is evenly divisible by 209 (we have 209 / 209 = 1, so the remainder of this division is indeed zero)
  • 418: indeed, 418 = 209 × 2
  • 627: indeed, 627 = 209 × 3
  • 836: indeed, 836 = 209 × 4
  • 1 045: indeed, 1 045 = 209 × 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 209). 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 about 14.457). 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 209

  • Preceding numbers: …207, 208
  • Following numbers: 210, 211

Nearest numbers from 209

  • Preceding prime number: 199
  • Following prime number: 211
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