Is 111 a prime number? What are the divisors of 111?

## Parity of 111

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

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## Is 111 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 111 is about 10.536.

Thus, the square root of 111 is not an integer, and therefore 111 is not a square number.

## What is the square number of 111?

The square of a number (here 111) is the result of the product of this number (111) by itself (i.e., 111 × 111); the square of 111 is sometimes called "raising 111 to the power 2", or "111 squared".

The square of 111 is 12 321 because 111 × 111 = 1112 = 12 321.

As a consequence, 111 is the square root of 12 321.

## Number of digits of 111

111 is a number with 3 digits.

## What are the multiples of 111?

The multiples of 111 are all integers evenly divisible by 111, that is all numbers such that the remainder of the division by 111 is zero. There are infinitely many multiples of 111. The smallest multiples of 111 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 111 too, since 0 × 111 = 0
• 111: indeed, 111 is a multiple of itself, since 111 is evenly divisible by 111 (we have 111 / 111 = 1, so the remainder of this division is indeed zero)
• 222: indeed, 222 = 111 × 2
• 333: indeed, 333 = 111 × 3
• 444: indeed, 444 = 111 × 4
• 555: indeed, 555 = 111 × 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 111). 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 10.536). 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 111

• Preceding numbers: …109, 110
• Following numbers: 112, 113

### Nearest numbers from 111

• Preceding prime number: 109
• Following prime number: 113
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