Is 472 a prime number?

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

For 472, the answer is: No, 472 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 472) is as follows: 1, 2, 4, 8, 59, 118, 236, 472.

For 472 to be a prime number, it would have been required that 472 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

472 is a multiple of 1
472 is a multiple of 2
472 is a multiple of 4
472 is a multiple of 8
472 is a multiple of 59
472 is a multiple of 118
472 is a multiple of 236

For 472 to be a prime number, it would have been required that 472 has only two divisors, i.e., itself and 1.

Is 472 a deficient number?

Yes, 472 is a deficient number, that is to say 472 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 472 without 472 itself (that is 1 + 2 + 4 + 8 + 59 + 118 + 236 = 428).

Parity of 472

472 is an even number, because it is evenly divisible by 2: 472 / 2 = 236.

Find out more:

What is an even number?

Is 472 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 472 is about 21.726.

Thus, the square root of 472 is not an integer, and therefore 472 is not a square number.

What is the square number of 472?

The square of a number (here 472) is the result of the product of this number (472) by itself (i.e., 472 × 472); the square of 472 is sometimes called "raising 472 to the power 2", or "472 squared".

The square of 472 is 222 784 because 472 × 472 = 472² = 222 784.

As a consequence, 472 is the square root of 222 784.

Number of digits of 472

472 is a number with 3 digits.

What are the multiples of 472?

The multiples of 472 are all integers evenly divisible by 472, that is all numbers such that the remainder of the division by 472 is zero. There are infinitely many multiples of 472. The smallest multiples of 472 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 472 too, since 0 × 472 = 0
472: indeed, 472 is a multiple of itself, since 472 is evenly divisible by 472 (we have 472 / 472 = 1, so the remainder of this division is indeed zero)
944: indeed, 944 = 472 × 2
1 416: indeed, 1 416 = 472 × 3
1 888: indeed, 1 888 = 472 × 4
2 360: indeed, 2 360 = 472 × 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 472). 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 21.726). 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 472

Preceding numbers: …470, 471
Following numbers: 473, 474…

Nearest numbers from 472

Preceding prime number: 467
Following prime number: 479