Is 403 a prime number?

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

For 403, the answer is: No, 403 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 403) is as follows: 1, 13, 31, 403.

For 403 to be a prime number, it would have been required that 403 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

403 is a multiple of 1
403 is a multiple of 13
403 is a multiple of 31

For 403 to be a prime number, it would have been required that 403 has only two divisors, i.e., itself and 1.

However, 403 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 403 = 13 x 31, where 13 and 31 are both prime numbers.

Is 403 a deficient number?

Yes, 403 is a deficient number, that is to say 403 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 403 without 403 itself (that is 1 + 13 + 31 = 45).

Parity of 403

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

Find out more:

What is an even number?

Is 403 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 403 is about 20.075.

Thus, the square root of 403 is not an integer, and therefore 403 is not a square number.

What is the square number of 403?

The square of a number (here 403) is the result of the product of this number (403) by itself (i.e., 403 × 403); the square of 403 is sometimes called "raising 403 to the power 2", or "403 squared".

The square of 403 is 162 409 because 403 × 403 = 403² = 162 409.

As a consequence, 403 is the square root of 162 409.

Number of digits of 403

403 is a number with 3 digits.

What are the multiples of 403?

The multiples of 403 are all integers evenly divisible by 403, that is all numbers such that the remainder of the division by 403 is zero. There are infinitely many multiples of 403. The smallest multiples of 403 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 403 too, since 0 × 403 = 0
403: indeed, 403 is a multiple of itself, since 403 is evenly divisible by 403 (we have 403 / 403 = 1, so the remainder of this division is indeed zero)
806: indeed, 806 = 403 × 2
1 209: indeed, 1 209 = 403 × 3
1 612: indeed, 1 612 = 403 × 4
2 015: indeed, 2 015 = 403 × 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 403). 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 20.075). 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 403

Preceding numbers: …401, 402
Following numbers: 404, 405…

Nearest numbers from 403

Preceding prime number: 401
Following prime number: 409