Is 465 a prime number?

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

For 465, the answer is: No, 465 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 465) is as follows: 1, 3, 5, 15, 31, 93, 155, 465.

For 465 to be a prime number, it would have been required that 465 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 465 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 465 is 5, so it is divisible by 5 and is therefore not prime.

As a consequence:

465 is a multiple of 1
465 is a multiple of 3
465 is a multiple of 5
465 is a multiple of 15
465 is a multiple of 31
465 is a multiple of 93
465 is a multiple of 155

For 465 to be a prime number, it would have been required that 465 has only two divisors, i.e., itself and 1.

Is 465 a deficient number?

Yes, 465 is a deficient number, that is to say 465 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 465 without 465 itself (that is 1 + 3 + 5 + 15 + 31 + 93 + 155 = 303).

Parity of 465

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

Find out more:

What is an even number?

Is 465 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 465 is about 21.564.

Thus, the square root of 465 is not an integer, and therefore 465 is not a square number.

What is the square number of 465?

The square of a number (here 465) is the result of the product of this number (465) by itself (i.e., 465 × 465); the square of 465 is sometimes called "raising 465 to the power 2", or "465 squared".

The square of 465 is 216 225 because 465 × 465 = 465² = 216 225.

As a consequence, 465 is the square root of 216 225.

Number of digits of 465

465 is a number with 3 digits.

What are the multiples of 465?

The multiples of 465 are all integers evenly divisible by 465, that is all numbers such that the remainder of the division by 465 is zero. There are infinitely many multiples of 465. The smallest multiples of 465 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 465 too, since 0 × 465 = 0
465: indeed, 465 is a multiple of itself, since 465 is evenly divisible by 465 (we have 465 / 465 = 1, so the remainder of this division is indeed zero)
930: indeed, 930 = 465 × 2
1 395: indeed, 1 395 = 465 × 3
1 860: indeed, 1 860 = 465 × 4
2 325: indeed, 2 325 = 465 × 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 465). 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 21.564). 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 465

Preceding numbers: …463, 464
Following numbers: 466, 467…

Nearest numbers from 465

Preceding prime number: 463
Following prime number: 467