Is 468 a prime number?

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

For 468, the answer is: No, 468 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 468) is as follows: 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468.

For 468 to be a prime number, it would have been required that 468 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

468 is a multiple of 1
468 is a multiple of 2
468 is a multiple of 3
468 is a multiple of 4
468 is a multiple of 6
468 is a multiple of 9
468 is a multiple of 12
468 is a multiple of 13
468 is a multiple of 18
468 is a multiple of 26
468 is a multiple of 36
468 is a multiple of 39
468 is a multiple of 52
468 is a multiple of 78
468 is a multiple of 117
468 is a multiple of 156
468 is a multiple of 234

For 468 to be a prime number, it would have been required that 468 has only two divisors, i.e., itself and 1.

Is 468 a deficient number?

No, 468 is not a deficient number: to be deficient, 468 should have been such that 468 is larger than the sum of its proper divisors, i.e., the divisors of 468 without 468 itself (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 13 + 18 + 26 + 36 + 39 + 52 + 78 + 117 + 156 + 234 = 806).

In fact, 468 is an abundant number; 468 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 13 + 18 + 26 + 36 + 39 + 52 + 78 + 117 + 156 + 234 = 806). The smallest abundant number is 12.

Parity of 468

468 is an even number, because it is evenly divisible by 2: 468 / 2 = 234.

Find out more:

What is an even number?

Is 468 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 468 is about 21.633.

Thus, the square root of 468 is not an integer, and therefore 468 is not a square number.

What is the square number of 468?

The square of a number (here 468) is the result of the product of this number (468) by itself (i.e., 468 × 468); the square of 468 is sometimes called "raising 468 to the power 2", or "468 squared".

The square of 468 is 219 024 because 468 × 468 = 468² = 219 024.

As a consequence, 468 is the square root of 219 024.

Number of digits of 468

468 is a number with 3 digits.

What are the multiples of 468?

The multiples of 468 are all integers evenly divisible by 468, that is all numbers such that the remainder of the division by 468 is zero. There are infinitely many multiples of 468. The smallest multiples of 468 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 468 too, since 0 × 468 = 0
468: indeed, 468 is a multiple of itself, since 468 is evenly divisible by 468 (we have 468 / 468 = 1, so the remainder of this division is indeed zero)
936: indeed, 936 = 468 × 2
1 404: indeed, 1 404 = 468 × 3
1 872: indeed, 1 872 = 468 × 4
2 340: indeed, 2 340 = 468 × 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 468). 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 21.633). 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 468

Preceding numbers: …466, 467
Following numbers: 469, 470…

Nearest numbers from 468

Preceding prime number: 467
Following prime number: 479