Is 81 a prime number? What are the divisors of 81?

## Is 81 a prime number?

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

For 81, the answer is: No, 81 is not a prime number.

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

To be 81 a prime number, it would have been required that 81 has only two divisors, i.e., itself and 1.

As a consequence:

• 81 is a multiple of 1
• 81 is a multiple of 3
• 81 is a multiple of 9
• 81 is a multiple of 27

To be 81 a prime number, it would have been required that 81 has only two divisors, i.e., itself and 1.

## Is 81 a deficient number?

Yes, 81 is a deficient number, that is to say 81 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 81 without 81 itself (that is 1 + 3 + 9 + 27 = 40).

## Parity of 81

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

## Is 81 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 81 is 9.

Therefore, the square root of 81 is an integer, and as a consequence 81 is a perfect square.

As a consequence, 9 is the square root of 81.

## What is the square number of 81?

The square of a number (here 81) is the result of the product of this number (81) by itself (i.e., 81 × 81); the square of 81 is sometimes called "raising 81 to the power 2", or "81 squared".

The square of 81 is 6 561 because 81 × 81 = 812 = 6 561.

As a consequence, 81 is the square root of 6 561.

## Number of digits of 81

81 is a number with 2 digits.

## What are the multiples of 81?

The multiples of 81 are all integers evenly divisible by 81, that is all numbers such that the remainder of the division by 81 is zero. There are infinitely many multiples of 81. The smallest multiples of 81 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 81 too, since 0 × 81 = 0
• 81: indeed, 81 is a multiple of itself, since 81 is evenly divisible by 81 (we have 81 / 81 = 1, so the remainder of this division is indeed zero)
• 162: indeed, 162 = 81 × 2
• 243: indeed, 243 = 81 × 3
• 324: indeed, 324 = 81 × 4
• 405: indeed, 405 = 81 × 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 81). 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 9). 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 81

• Preceding numbers: …79, 80
• Following numbers: 82, 83

## Nearest numbers from 81

• Preceding prime number: 79
• Following prime number: 83
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