Is 408 a prime number?

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

For 408, the answer is: No, 408 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 408) is as follows: 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408.

For 408 to be a prime number, it would have been required that 408 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

408 is a multiple of 1
408 is a multiple of 2
408 is a multiple of 3
408 is a multiple of 4
408 is a multiple of 6
408 is a multiple of 8
408 is a multiple of 12
408 is a multiple of 17
408 is a multiple of 24
408 is a multiple of 34
408 is a multiple of 51
408 is a multiple of 68
408 is a multiple of 102
408 is a multiple of 136
408 is a multiple of 204

For 408 to be a prime number, it would have been required that 408 has only two divisors, i.e., itself and 1.

Is 408 a deficient number?

No, 408 is not a deficient number: to be deficient, 408 should have been such that 408 is larger than the sum of its proper divisors, i.e., the divisors of 408 without 408 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 17 + 24 + 34 + 51 + 68 + 102 + 136 + 204 = 672).

In fact, 408 is an abundant number; 408 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 17 + 24 + 34 + 51 + 68 + 102 + 136 + 204 = 672). The smallest abundant number is 12.

Parity of 408

408 is an even number, because it is evenly divisible by 2: 408 / 2 = 204.

Find out more:

What is an even number?

Is 408 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 408 is about 20.199.

Thus, the square root of 408 is not an integer, and therefore 408 is not a square number.

What is the square number of 408?

The square of a number (here 408) is the result of the product of this number (408) by itself (i.e., 408 × 408); the square of 408 is sometimes called "raising 408 to the power 2", or "408 squared".

The square of 408 is 166 464 because 408 × 408 = 408² = 166 464.

As a consequence, 408 is the square root of 166 464.

Number of digits of 408

408 is a number with 3 digits.

What are the multiples of 408?

The multiples of 408 are all integers evenly divisible by 408, that is all numbers such that the remainder of the division by 408 is zero. There are infinitely many multiples of 408. The smallest multiples of 408 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 408 too, since 0 × 408 = 0
408: indeed, 408 is a multiple of itself, since 408 is evenly divisible by 408 (we have 408 / 408 = 1, so the remainder of this division is indeed zero)
816: indeed, 816 = 408 × 2
1 224: indeed, 1 224 = 408 × 3
1 632: indeed, 1 632 = 408 × 4
2 040: indeed, 2 040 = 408 × 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 408). 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 20.199). 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 408

Preceding numbers: …406, 407
Following numbers: 409, 410…

Nearest numbers from 408

Preceding prime number: 401
Following prime number: 409