Is 461 a prime number?

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

Find out more:

• What is an even 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 461 is about 21.471.

Thus, the square root of 461 is not an integer, and therefore 461 is not a square number.

Anyway, 461 is a prime number, and a prime number cannot be a perfect square.

The square of a number (here 461) is the result of the product of this number (461) by itself (i.e., 461 × 461); the square of 461 is sometimes called "raising 461 to the power 2", or "461 squared".

The square of 461 is 212 521 because 461 × 461 = 461² = 212 521.

As a consequence, 461 is the square root of 212 521.

461 is a number with 3 digits.

The multiples of 461 are all integers evenly divisible by 461, that is all numbers such that the remainder of the division by 461 is zero. There are infinitely many multiples of 461. The smallest multiples of 461 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 461 too, since 0 × 461 = 0
• 461: indeed, 461 is a multiple of itself, since 461 is evenly divisible by 461 (we have 461 / 461 = 1, so the remainder of this division is indeed zero)
• 922: indeed, 922 = 461 × 2
• 1 383: indeed, 1 383 = 461 × 3
• 1 844: indeed, 1 844 = 461 × 4
• 2 305: indeed, 2 305 = 461 × 5
• etc.

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 461). 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 21.471). 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.

• Preceding numbers: …459, 460
• Following numbers: 462, 463…

Nearest numbers from 461

• Preceding prime number: 457
• Following prime number: 463

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• 461 est-il un nombre premier ?