Is 478 a prime number?

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

For 478, the answer is: No, 478 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 478) is as follows: 1, 2, 239, 478.

For 478 to be a prime number, it would have been required that 478 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

478 is a multiple of 1
478 is a multiple of 2
478 is a multiple of 239

For 478 to be a prime number, it would have been required that 478 has only two divisors, i.e., itself and 1.

However, 478 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 478 = 2 x 239, where 2 and 239 are both prime numbers.

Is 478 a deficient number?

Yes, 478 is a deficient number, that is to say 478 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 478 without 478 itself (that is 1 + 2 + 239 = 242).

Parity of 478

478 is an even number, because it is evenly divisible by 2: 478 / 2 = 239.

Find out more:

What is an even number?

Is 478 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 478 is about 21.863.

Thus, the square root of 478 is not an integer, and therefore 478 is not a square number.

What is the square number of 478?

The square of a number (here 478) is the result of the product of this number (478) by itself (i.e., 478 × 478); the square of 478 is sometimes called "raising 478 to the power 2", or "478 squared".

The square of 478 is 228 484 because 478 × 478 = 478² = 228 484.

As a consequence, 478 is the square root of 228 484.

Number of digits of 478

478 is a number with 3 digits.

What are the multiples of 478?

The multiples of 478 are all integers evenly divisible by 478, that is all numbers such that the remainder of the division by 478 is zero. There are infinitely many multiples of 478. The smallest multiples of 478 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 478 too, since 0 × 478 = 0
478: indeed, 478 is a multiple of itself, since 478 is evenly divisible by 478 (we have 478 / 478 = 1, so the remainder of this division is indeed zero)
956: indeed, 956 = 478 × 2
1 434: indeed, 1 434 = 478 × 3
1 912: indeed, 1 912 = 478 × 4
2 390: indeed, 2 390 = 478 × 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 478). 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 21.863). 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 478

Preceding numbers: …476, 477
Following numbers: 479, 480…

Nearest numbers from 478

Preceding prime number: 467
Following prime number: 479