Is 480 a prime number?

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

For 480, the answer is: No, 480 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 480) is as follows: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480.

For 480 to be a prime number, it would have been required that 480 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 480 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 480 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

480 is a multiple of 1
480 is a multiple of 2
480 is a multiple of 3
480 is a multiple of 4
480 is a multiple of 5
480 is a multiple of 6
480 is a multiple of 8
480 is a multiple of 10
480 is a multiple of 12
480 is a multiple of 15
480 is a multiple of 16
480 is a multiple of 20
480 is a multiple of 24
480 is a multiple of 30
480 is a multiple of 32
480 is a multiple of 40
480 is a multiple of 48
480 is a multiple of 60
480 is a multiple of 80
480 is a multiple of 96
480 is a multiple of 120
480 is a multiple of 160
480 is a multiple of 240

For 480 to be a prime number, it would have been required that 480 has only two divisors, i.e., itself and 1.

Is 480 a deficient number?

No, 480 is not a deficient number: to be deficient, 480 should have been such that 480 is larger than the sum of its proper divisors, i.e., the divisors of 480 without 480 itself (that is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 40 + 48 + 60 + 80 + 96 + 120 + 160 + 240 = 1 032).

In fact, 480 is an abundant number; 480 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 40 + 48 + 60 + 80 + 96 + 120 + 160 + 240 = 1 032). The smallest abundant number is 12.

Parity of 480

480 is an even number, because it is evenly divisible by 2: 480 / 2 = 240.

Find out more:

What is an even number?

Is 480 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 480 is about 21.909.

Thus, the square root of 480 is not an integer, and therefore 480 is not a square number.

What is the square number of 480?

The square of a number (here 480) is the result of the product of this number (480) by itself (i.e., 480 × 480); the square of 480 is sometimes called "raising 480 to the power 2", or "480 squared".

The square of 480 is 230 400 because 480 × 480 = 480² = 230 400.

As a consequence, 480 is the square root of 230 400.

Number of digits of 480

480 is a number with 3 digits.

What are the multiples of 480?

The multiples of 480 are all integers evenly divisible by 480, that is all numbers such that the remainder of the division by 480 is zero. There are infinitely many multiples of 480. The smallest multiples of 480 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 480 too, since 0 × 480 = 0
480: indeed, 480 is a multiple of itself, since 480 is evenly divisible by 480 (we have 480 / 480 = 1, so the remainder of this division is indeed zero)
960: indeed, 960 = 480 × 2
1 440: indeed, 1 440 = 480 × 3
1 920: indeed, 1 920 = 480 × 4
2 400: indeed, 2 400 = 480 × 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 480). 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 21.909). 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 480

Preceding numbers: …478, 479
Following numbers: 481, 482…

Nearest numbers from 480

Preceding prime number: 479
Following prime number: 487