Is 413 a prime number?

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

For 413, the answer is: No, 413 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 413) is as follows: 1, 7, 59, 413.

For 413 to be a prime number, it would have been required that 413 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

413 is a multiple of 1
413 is a multiple of 7
413 is a multiple of 59

For 413 to be a prime number, it would have been required that 413 has only two divisors, i.e., itself and 1.

However, 413 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 413 = 7 x 59, where 7 and 59 are both prime numbers.

Is 413 a deficient number?

Yes, 413 is a deficient number, that is to say 413 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 413 without 413 itself (that is 1 + 7 + 59 = 67).

Parity of 413

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

Find out more:

What is an even number?

Is 413 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 413 is about 20.322.

Thus, the square root of 413 is not an integer, and therefore 413 is not a square number.

What is the square number of 413?

The square of a number (here 413) is the result of the product of this number (413) by itself (i.e., 413 × 413); the square of 413 is sometimes called "raising 413 to the power 2", or "413 squared".

The square of 413 is 170 569 because 413 × 413 = 413² = 170 569.

As a consequence, 413 is the square root of 170 569.

Number of digits of 413

413 is a number with 3 digits.

What are the multiples of 413?

The multiples of 413 are all integers evenly divisible by 413, that is all numbers such that the remainder of the division by 413 is zero. There are infinitely many multiples of 413. The smallest multiples of 413 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 413 too, since 0 × 413 = 0
413: indeed, 413 is a multiple of itself, since 413 is evenly divisible by 413 (we have 413 / 413 = 1, so the remainder of this division is indeed zero)
826: indeed, 826 = 413 × 2
1 239: indeed, 1 239 = 413 × 3
1 652: indeed, 1 652 = 413 × 4
2 065: indeed, 2 065 = 413 × 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 413). 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 20.322). 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 413

Preceding numbers: …411, 412
Following numbers: 414, 415…

Nearest numbers from 413

Preceding prime number: 409
Following prime number: 419