Is 261 a prime number?

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

For 261, the answer is: No, 261 is not a prime number.

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

For 261 to be a prime number, it would have been required that 261 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

261 is a multiple of 1
261 is a multiple of 3
261 is a multiple of 9
261 is a multiple of 29
261 is a multiple of 87

For 261 to be a prime number, it would have been required that 261 has only two divisors, i.e., itself and 1.

Is 261 a deficient number?

Yes, 261 is a deficient number, that is to say 261 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 261 without 261 itself (that is 1 + 3 + 9 + 29 + 87 = 129).

Parity of 261

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

Find out more:

What is an even number?

Is 261 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 261 is about 16.155.

Thus, the square root of 261 is not an integer, and therefore 261 is not a square number.

What is the square number of 261?

The square of a number (here 261) is the result of the product of this number (261) by itself (i.e., 261 × 261); the square of 261 is sometimes called "raising 261 to the power 2", or "261 squared".

The square of 261 is 68 121 because 261 × 261 = 261² = 68 121.

As a consequence, 261 is the square root of 68 121.

Number of digits of 261

261 is a number with 3 digits.

What are the multiples of 261?

The multiples of 261 are all integers evenly divisible by 261, that is all numbers such that the remainder of the division by 261 is zero. There are infinitely many multiples of 261. The smallest multiples of 261 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 261 too, since 0 × 261 = 0
261: indeed, 261 is a multiple of itself, since 261 is evenly divisible by 261 (we have 261 / 261 = 1, so the remainder of this division is indeed zero)
522: indeed, 522 = 261 × 2
783: indeed, 783 = 261 × 3
1 044: indeed, 1 044 = 261 × 4
1 305: indeed, 1 305 = 261 × 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 261). 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 16.155). 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 261

Preceding numbers: …259, 260
Following numbers: 262, 263…

Nearest numbers from 261

Preceding prime number: 257
Following prime number: 263