Is 567 a prime number?

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

For 567, the answer is: No, 567 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 567) is as follows: 1, 3, 7, 9, 21, 27, 63, 81, 189, 567.

For 567 to be a prime number, it would have been required that 567 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

567 is a multiple of 1
567 is a multiple of 3
567 is a multiple of 7
567 is a multiple of 9
567 is a multiple of 21
567 is a multiple of 27
567 is a multiple of 63
567 is a multiple of 81
567 is a multiple of 189

For 567 to be a prime number, it would have been required that 567 has only two divisors, i.e., itself and 1.

Is 567 a deficient number?

Yes, 567 is a deficient number, that is to say 567 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 567 without 567 itself (that is 1 + 3 + 7 + 9 + 21 + 27 + 63 + 81 + 189 = 401).

Parity of 567

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

Find out more:

What is an even number?

Is 567 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 567 is about 23.812.

Thus, the square root of 567 is not an integer, and therefore 567 is not a square number.

What is the square number of 567?

The square of a number (here 567) is the result of the product of this number (567) by itself (i.e., 567 × 567); the square of 567 is sometimes called "raising 567 to the power 2", or "567 squared".

The square of 567 is 321 489 because 567 × 567 = 567² = 321 489.

As a consequence, 567 is the square root of 321 489.

Number of digits of 567

567 is a number with 3 digits.

What are the multiples of 567?

The multiples of 567 are all integers evenly divisible by 567, that is all numbers such that the remainder of the division by 567 is zero. There are infinitely many multiples of 567. The smallest multiples of 567 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 567 too, since 0 × 567 = 0
567: indeed, 567 is a multiple of itself, since 567 is evenly divisible by 567 (we have 567 / 567 = 1, so the remainder of this division is indeed zero)
1 134: indeed, 1 134 = 567 × 2
1 701: indeed, 1 701 = 567 × 3
2 268: indeed, 2 268 = 567 × 4
2 835: indeed, 2 835 = 567 × 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 567). 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 23.812). 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 567

Preceding numbers: …565, 566
Following numbers: 568, 569…

Nearest numbers from 567

Preceding prime number: 563
Following prime number: 569