Is 213 a prime number?

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

For 213, the answer is: No, 213 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 213) is as follows: 1, 3, 71, 213.

For 213 to be a prime number, it would have been required that 213 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

213 is a multiple of 1
213 is a multiple of 3
213 is a multiple of 71

For 213 to be a prime number, it would have been required that 213 has only two divisors, i.e., itself and 1.

However, 213 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 213 = 3 x 71, where 3 and 71 are both prime numbers.

Is 213 a deficient number?

Yes, 213 is a deficient number, that is to say 213 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 213 without 213 itself (that is 1 + 3 + 71 = 75).

Parity of 213

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

Find out more:

What is an even number?

Is 213 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 213 is about 14.595.

Thus, the square root of 213 is not an integer, and therefore 213 is not a square number.

What is the square number of 213?

The square of a number (here 213) is the result of the product of this number (213) by itself (i.e., 213 × 213); the square of 213 is sometimes called "raising 213 to the power 2", or "213 squared".

The square of 213 is 45 369 because 213 × 213 = 213² = 45 369.

As a consequence, 213 is the square root of 45 369.

Number of digits of 213

213 is a number with 3 digits.

What are the multiples of 213?

The multiples of 213 are all integers evenly divisible by 213, that is all numbers such that the remainder of the division by 213 is zero. There are infinitely many multiples of 213. The smallest multiples of 213 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 213 too, since 0 × 213 = 0
213: indeed, 213 is a multiple of itself, since 213 is evenly divisible by 213 (we have 213 / 213 = 1, so the remainder of this division is indeed zero)
426: indeed, 426 = 213 × 2
639: indeed, 639 = 213 × 3
852: indeed, 852 = 213 × 4
1 065: indeed, 1 065 = 213 × 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 213). 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 14.595). 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 213

Preceding numbers: …211, 212
Following numbers: 214, 215…

Nearest numbers from 213

Preceding prime number: 211
Following prime number: 223