Is 413 a prime number? What are the divisors of 413?

## Parity of 413

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

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## 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:

## 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
Find out whether some integer is a prime number