Is 310 a prime number?

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

For 310, the answer is: No, 310 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 310) is as follows: 1, 2, 5, 10, 31, 62, 155, 310.

For 310 to be a prime number, it would have been required that 310 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 310 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 310 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

310 is a multiple of 1
310 is a multiple of 2
310 is a multiple of 5
310 is a multiple of 10
310 is a multiple of 31
310 is a multiple of 62
310 is a multiple of 155

For 310 to be a prime number, it would have been required that 310 has only two divisors, i.e., itself and 1.

Is 310 a deficient number?

Yes, 310 is a deficient number, that is to say 310 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 310 without 310 itself (that is 1 + 2 + 5 + 10 + 31 + 62 + 155 = 266).

Parity of 310

310 is an even number, because it is evenly divisible by 2: 310 / 2 = 155.

Find out more:

What is an even number?

Is 310 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 310 is about 17.607.

Thus, the square root of 310 is not an integer, and therefore 310 is not a square number.

What is the square number of 310?

The square of a number (here 310) is the result of the product of this number (310) by itself (i.e., 310 × 310); the square of 310 is sometimes called "raising 310 to the power 2", or "310 squared".

The square of 310 is 96 100 because 310 × 310 = 310² = 96 100.

As a consequence, 310 is the square root of 96 100.

Number of digits of 310

310 is a number with 3 digits.

What are the multiples of 310?

The multiples of 310 are all integers evenly divisible by 310, that is all numbers such that the remainder of the division by 310 is zero. There are infinitely many multiples of 310. The smallest multiples of 310 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 310 too, since 0 × 310 = 0
310: indeed, 310 is a multiple of itself, since 310 is evenly divisible by 310 (we have 310 / 310 = 1, so the remainder of this division is indeed zero)
620: indeed, 620 = 310 × 2
930: indeed, 930 = 310 × 3
1 240: indeed, 1 240 = 310 × 4
1 550: indeed, 1 550 = 310 × 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 310). 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 17.607). 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 310

Preceding numbers: …308, 309
Following numbers: 311, 312…

Nearest numbers from 310

Preceding prime number: 307
Following prime number: 311