Is 473 a prime number?

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

For 473, the answer is: No, 473 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 473) is as follows: 1, 11, 43, 473.

For 473 to be a prime number, it would have been required that 473 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

473 is a multiple of 1
473 is a multiple of 11
473 is a multiple of 43

For 473 to be a prime number, it would have been required that 473 has only two divisors, i.e., itself and 1.

However, 473 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 473 = 11 x 43, where 11 and 43 are both prime numbers.

Is 473 a deficient number?

Yes, 473 is a deficient number, that is to say 473 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 473 without 473 itself (that is 1 + 11 + 43 = 55).

Parity of 473

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

Find out more:

What is an even number?

Is 473 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 473 is about 21.749.

Thus, the square root of 473 is not an integer, and therefore 473 is not a square number.

What is the square number of 473?

The square of a number (here 473) is the result of the product of this number (473) by itself (i.e., 473 × 473); the square of 473 is sometimes called "raising 473 to the power 2", or "473 squared".

The square of 473 is 223 729 because 473 × 473 = 473² = 223 729.

As a consequence, 473 is the square root of 223 729.

Number of digits of 473

473 is a number with 3 digits.

What are the multiples of 473?

The multiples of 473 are all integers evenly divisible by 473, that is all numbers such that the remainder of the division by 473 is zero. There are infinitely many multiples of 473. The smallest multiples of 473 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 473 too, since 0 × 473 = 0
473: indeed, 473 is a multiple of itself, since 473 is evenly divisible by 473 (we have 473 / 473 = 1, so the remainder of this division is indeed zero)
946: indeed, 946 = 473 × 2
1 419: indeed, 1 419 = 473 × 3
1 892: indeed, 1 892 = 473 × 4
2 365: indeed, 2 365 = 473 × 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 473). 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 21.749). 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 473

Preceding numbers: …471, 472
Following numbers: 474, 475…

Nearest numbers from 473

Preceding prime number: 467
Following prime number: 479