Is 123 a prime number? What are the divisors of 123?

## Parity of 123

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

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## Is 123 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 123 is about 11.091.

Thus, the square root of 123 is not an integer, and therefore 123 is not a square number.

## What is the square number of 123?

The square of a number (here 123) is the result of the product of this number (123) by itself (i.e., 123 × 123); the square of 123 is sometimes called "raising 123 to the power 2", or "123 squared".

The square of 123 is 15 129 because 123 × 123 = 1232 = 15 129.

As a consequence, 123 is the square root of 15 129.

## Number of digits of 123

123 is a number with 3 digits.

## What are the multiples of 123?

The multiples of 123 are all integers evenly divisible by 123, that is all numbers such that the remainder of the division by 123 is zero. There are infinitely many multiples of 123. The smallest multiples of 123 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 123 too, since 0 × 123 = 0
• 123: indeed, 123 is a multiple of itself, since 123 is evenly divisible by 123 (we have 123 / 123 = 1, so the remainder of this division is indeed zero)
• 246: indeed, 246 = 123 × 2
• 369: indeed, 369 = 123 × 3
• 492: indeed, 492 = 123 × 4
• 615: indeed, 615 = 123 × 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 123). 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 11.091). 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 123

• Preceding numbers: …121, 122
• Following numbers: 124, 125

### Nearest numbers from 123

• Preceding prime number: 113
• Following prime number: 127
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