Is 522 a prime number?

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

For 522, the answer is: No, 522 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 522) is as follows: 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522.

For 522 to be a prime number, it would have been required that 522 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

522 is a multiple of 1
522 is a multiple of 2
522 is a multiple of 3
522 is a multiple of 6
522 is a multiple of 9
522 is a multiple of 18
522 is a multiple of 29
522 is a multiple of 58
522 is a multiple of 87
522 is a multiple of 174
522 is a multiple of 261

For 522 to be a prime number, it would have been required that 522 has only two divisors, i.e., itself and 1.

Is 522 a deficient number?

No, 522 is not a deficient number: to be deficient, 522 should have been such that 522 is larger than the sum of its proper divisors, i.e., the divisors of 522 without 522 itself (that is 1 + 2 + 3 + 6 + 9 + 18 + 29 + 58 + 87 + 174 + 261 = 648).

In fact, 522 is an abundant number; 522 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 9 + 18 + 29 + 58 + 87 + 174 + 261 = 648). The smallest abundant number is 12.

Parity of 522

522 is an even number, because it is evenly divisible by 2: 522 / 2 = 261.

Find out more:

What is an even number?

Is 522 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 522 is about 22.847.

Thus, the square root of 522 is not an integer, and therefore 522 is not a square number.

What is the square number of 522?

The square of a number (here 522) is the result of the product of this number (522) by itself (i.e., 522 × 522); the square of 522 is sometimes called "raising 522 to the power 2", or "522 squared".

The square of 522 is 272 484 because 522 × 522 = 522² = 272 484.

As a consequence, 522 is the square root of 272 484.

Number of digits of 522

522 is a number with 3 digits.

What are the multiples of 522?

The multiples of 522 are all integers evenly divisible by 522, that is all numbers such that the remainder of the division by 522 is zero. There are infinitely many multiples of 522. The smallest multiples of 522 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 522 too, since 0 × 522 = 0
522: indeed, 522 is a multiple of itself, since 522 is evenly divisible by 522 (we have 522 / 522 = 1, so the remainder of this division is indeed zero)
1 044: indeed, 1 044 = 522 × 2
1 566: indeed, 1 566 = 522 × 3
2 088: indeed, 2 088 = 522 × 4
2 610: indeed, 2 610 = 522 × 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 522). 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 22.847). 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 522

Preceding numbers: …520, 521
Following numbers: 523, 524…

Nearest numbers from 522

Preceding prime number: 521
Following prime number: 523