Is 260 a prime number?

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

For 260, the answer is: No, 260 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 260) is as follows: 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260.

For 260 to be a prime number, it would have been required that 260 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 260 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 260 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

260 is a multiple of 1
260 is a multiple of 2
260 is a multiple of 4
260 is a multiple of 5
260 is a multiple of 10
260 is a multiple of 13
260 is a multiple of 20
260 is a multiple of 26
260 is a multiple of 52
260 is a multiple of 65
260 is a multiple of 130

For 260 to be a prime number, it would have been required that 260 has only two divisors, i.e., itself and 1.

Is 260 a deficient number?

No, 260 is not a deficient number: to be deficient, 260 should have been such that 260 is larger than the sum of its proper divisors, i.e., the divisors of 260 without 260 itself (that is 1 + 2 + 4 + 5 + 10 + 13 + 20 + 26 + 52 + 65 + 130 = 328).

In fact, 260 is an abundant number; 260 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 10 + 13 + 20 + 26 + 52 + 65 + 130 = 328). The smallest abundant number is 12.

Parity of 260

260 is an even number, because it is evenly divisible by 2: 260 / 2 = 130.

Find out more:

What is an even number?

Is 260 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 260 is about 16.125.

Thus, the square root of 260 is not an integer, and therefore 260 is not a square number.

What is the square number of 260?

The square of a number (here 260) is the result of the product of this number (260) by itself (i.e., 260 × 260); the square of 260 is sometimes called "raising 260 to the power 2", or "260 squared".

The square of 260 is 67 600 because 260 × 260 = 260² = 67 600.

As a consequence, 260 is the square root of 67 600.

Number of digits of 260

260 is a number with 3 digits.

What are the multiples of 260?

The multiples of 260 are all integers evenly divisible by 260, that is all numbers such that the remainder of the division by 260 is zero. There are infinitely many multiples of 260. The smallest multiples of 260 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 260 too, since 0 × 260 = 0
260: indeed, 260 is a multiple of itself, since 260 is evenly divisible by 260 (we have 260 / 260 = 1, so the remainder of this division is indeed zero)
520: indeed, 520 = 260 × 2
780: indeed, 780 = 260 × 3
1 040: indeed, 1 040 = 260 × 4
1 300: indeed, 1 300 = 260 × 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 260). 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 16.125). 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 260

Preceding numbers: …258, 259
Following numbers: 261, 262…

Nearest numbers from 260

Preceding prime number: 257
Following prime number: 263