Is 464 a prime number?

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

For 464, the answer is: No, 464 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 464) is as follows: 1, 2, 4, 8, 16, 29, 58, 116, 232, 464.

For 464 to be a prime number, it would have been required that 464 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

464 is a multiple of 1
464 is a multiple of 2
464 is a multiple of 4
464 is a multiple of 8
464 is a multiple of 16
464 is a multiple of 29
464 is a multiple of 58
464 is a multiple of 116
464 is a multiple of 232

For 464 to be a prime number, it would have been required that 464 has only two divisors, i.e., itself and 1.

Is 464 a deficient number?

No, 464 is not a deficient number: to be deficient, 464 should have been such that 464 is larger than the sum of its proper divisors, i.e., the divisors of 464 without 464 itself (that is 1 + 2 + 4 + 8 + 16 + 29 + 58 + 116 + 232 = 466).

In fact, 464 is an abundant number; 464 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 8 + 16 + 29 + 58 + 116 + 232 = 466). The smallest abundant number is 12.

Parity of 464

464 is an even number, because it is evenly divisible by 2: 464 / 2 = 232.

Find out more:

What is an even number?

Is 464 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 464 is about 21.541.

Thus, the square root of 464 is not an integer, and therefore 464 is not a square number.

What is the square number of 464?

The square of a number (here 464) is the result of the product of this number (464) by itself (i.e., 464 × 464); the square of 464 is sometimes called "raising 464 to the power 2", or "464 squared".

The square of 464 is 215 296 because 464 × 464 = 464² = 215 296.

As a consequence, 464 is the square root of 215 296.

Number of digits of 464

464 is a number with 3 digits.

What are the multiples of 464?

The multiples of 464 are all integers evenly divisible by 464, that is all numbers such that the remainder of the division by 464 is zero. There are infinitely many multiples of 464. The smallest multiples of 464 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 464 too, since 0 × 464 = 0
464: indeed, 464 is a multiple of itself, since 464 is evenly divisible by 464 (we have 464 / 464 = 1, so the remainder of this division is indeed zero)
928: indeed, 928 = 464 × 2
1 392: indeed, 1 392 = 464 × 3
1 856: indeed, 1 856 = 464 × 4
2 320: indeed, 2 320 = 464 × 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 464). 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 21.541). 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 464

Preceding numbers: …462, 463
Following numbers: 465, 466…

Nearest numbers from 464

Preceding prime number: 463
Following prime number: 467