Is 312 a prime number?

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

For 312, the answer is: No, 312 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 312) is as follows: 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312.

For 312 to be a prime number, it would have been required that 312 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

312 is a multiple of 1
312 is a multiple of 2
312 is a multiple of 3
312 is a multiple of 4
312 is a multiple of 6
312 is a multiple of 8
312 is a multiple of 12
312 is a multiple of 13
312 is a multiple of 24
312 is a multiple of 26
312 is a multiple of 39
312 is a multiple of 52
312 is a multiple of 78
312 is a multiple of 104
312 is a multiple of 156

For 312 to be a prime number, it would have been required that 312 has only two divisors, i.e., itself and 1.

Is 312 a deficient number?

No, 312 is not a deficient number: to be deficient, 312 should have been such that 312 is larger than the sum of its proper divisors, i.e., the divisors of 312 without 312 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 13 + 24 + 26 + 39 + 52 + 78 + 104 + 156 = 528).

In fact, 312 is an abundant number; 312 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 13 + 24 + 26 + 39 + 52 + 78 + 104 + 156 = 528). The smallest abundant number is 12.

Parity of 312

312 is an even number, because it is evenly divisible by 2: 312 / 2 = 156.

Find out more:

What is an even number?

Is 312 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 312 is about 17.664.

Thus, the square root of 312 is not an integer, and therefore 312 is not a square number.

What is the square number of 312?

The square of a number (here 312) is the result of the product of this number (312) by itself (i.e., 312 × 312); the square of 312 is sometimes called "raising 312 to the power 2", or "312 squared".

The square of 312 is 97 344 because 312 × 312 = 312² = 97 344.

As a consequence, 312 is the square root of 97 344.

Number of digits of 312

312 is a number with 3 digits.

What are the multiples of 312?

The multiples of 312 are all integers evenly divisible by 312, that is all numbers such that the remainder of the division by 312 is zero. There are infinitely many multiples of 312. The smallest multiples of 312 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 312 too, since 0 × 312 = 0
312: indeed, 312 is a multiple of itself, since 312 is evenly divisible by 312 (we have 312 / 312 = 1, so the remainder of this division is indeed zero)
624: indeed, 624 = 312 × 2
936: indeed, 936 = 312 × 3
1 248: indeed, 1 248 = 312 × 4
1 560: indeed, 1 560 = 312 × 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 312). 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 17.664). 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 312

Preceding numbers: …310, 311
Following numbers: 313, 314…

Nearest numbers from 312

Preceding prime number: 311
Following prime number: 313