Is 309 a prime number?

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

For 309, the answer is: No, 309 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 309) is as follows: 1, 3, 103, 309.

For 309 to be a prime number, it would have been required that 309 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

309 is a multiple of 1
309 is a multiple of 3
309 is a multiple of 103

For 309 to be a prime number, it would have been required that 309 has only two divisors, i.e., itself and 1.

However, 309 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 309 = 3 x 103, where 3 and 103 are both prime numbers.

Is 309 a deficient number?

Yes, 309 is a deficient number, that is to say 309 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 309 without 309 itself (that is 1 + 3 + 103 = 107).

Parity of 309

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

Find out more:

What is an even number?

Is 309 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 309 is about 17.578.

Thus, the square root of 309 is not an integer, and therefore 309 is not a square number.

What is the square number of 309?

The square of a number (here 309) is the result of the product of this number (309) by itself (i.e., 309 × 309); the square of 309 is sometimes called "raising 309 to the power 2", or "309 squared".

The square of 309 is 95 481 because 309 × 309 = 309² = 95 481.

As a consequence, 309 is the square root of 95 481.

Number of digits of 309

309 is a number with 3 digits.

What are the multiples of 309?

The multiples of 309 are all integers evenly divisible by 309, that is all numbers such that the remainder of the division by 309 is zero. There are infinitely many multiples of 309. The smallest multiples of 309 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 309 too, since 0 × 309 = 0
309: indeed, 309 is a multiple of itself, since 309 is evenly divisible by 309 (we have 309 / 309 = 1, so the remainder of this division is indeed zero)
618: indeed, 618 = 309 × 2
927: indeed, 927 = 309 × 3
1 236: indeed, 1 236 = 309 × 4
1 545: indeed, 1 545 = 309 × 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 309). 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 17.578). 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 309

Preceding numbers: …307, 308
Following numbers: 310, 311…

Nearest numbers from 309

Preceding prime number: 307
Following prime number: 311