Is 561 a prime number?

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

For 561, the answer is: No, 561 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 561) is as follows: 1, 3, 11, 17, 33, 51, 187, 561.

For 561 to be a prime number, it would have been required that 561 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

561 is a multiple of 1
561 is a multiple of 3
561 is a multiple of 11
561 is a multiple of 17
561 is a multiple of 33
561 is a multiple of 51
561 is a multiple of 187

For 561 to be a prime number, it would have been required that 561 has only two divisors, i.e., itself and 1.

Is 561 a deficient number?

Yes, 561 is a deficient number, that is to say 561 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 561 without 561 itself (that is 1 + 3 + 11 + 17 + 33 + 51 + 187 = 303).

Parity of 561

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

Find out more:

What is an even number?

Is 561 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 561 is about 23.685.

Thus, the square root of 561 is not an integer, and therefore 561 is not a square number.

What is the square number of 561?

The square of a number (here 561) is the result of the product of this number (561) by itself (i.e., 561 × 561); the square of 561 is sometimes called "raising 561 to the power 2", or "561 squared".

The square of 561 is 314 721 because 561 × 561 = 561² = 314 721.

As a consequence, 561 is the square root of 314 721.

Number of digits of 561

561 is a number with 3 digits.

What are the multiples of 561?

The multiples of 561 are all integers evenly divisible by 561, that is all numbers such that the remainder of the division by 561 is zero. There are infinitely many multiples of 561. The smallest multiples of 561 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 561 too, since 0 × 561 = 0
561: indeed, 561 is a multiple of itself, since 561 is evenly divisible by 561 (we have 561 / 561 = 1, so the remainder of this division is indeed zero)
1 122: indeed, 1 122 = 561 × 2
1 683: indeed, 1 683 = 561 × 3
2 244: indeed, 2 244 = 561 × 4
2 805: indeed, 2 805 = 561 × 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 561). 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 23.685). 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 561

Preceding numbers: …559, 560
Following numbers: 562, 563…

Nearest numbers from 561

Preceding prime number: 557
Following prime number: 563