Is 471 a prime number?

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

For 471, the answer is: No, 471 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 471) is as follows: 1, 3, 157, 471.

For 471 to be a prime number, it would have been required that 471 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

471 is a multiple of 1
471 is a multiple of 3
471 is a multiple of 157

For 471 to be a prime number, it would have been required that 471 has only two divisors, i.e., itself and 1.

However, 471 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 471 = 3 x 157, where 3 and 157 are both prime numbers.

Is 471 a deficient number?

Yes, 471 is a deficient number, that is to say 471 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 471 without 471 itself (that is 1 + 3 + 157 = 161).

Parity of 471

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

Find out more:

What is an even number?

Is 471 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 471 is about 21.703.

Thus, the square root of 471 is not an integer, and therefore 471 is not a square number.

What is the square number of 471?

The square of a number (here 471) is the result of the product of this number (471) by itself (i.e., 471 × 471); the square of 471 is sometimes called "raising 471 to the power 2", or "471 squared".

The square of 471 is 221 841 because 471 × 471 = 471² = 221 841.

As a consequence, 471 is the square root of 221 841.

Number of digits of 471

471 is a number with 3 digits.

What are the multiples of 471?

The multiples of 471 are all integers evenly divisible by 471, that is all numbers such that the remainder of the division by 471 is zero. There are infinitely many multiples of 471. The smallest multiples of 471 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 471 too, since 0 × 471 = 0
471: indeed, 471 is a multiple of itself, since 471 is evenly divisible by 471 (we have 471 / 471 = 1, so the remainder of this division is indeed zero)
942: indeed, 942 = 471 × 2
1 413: indeed, 1 413 = 471 × 3
1 884: indeed, 1 884 = 471 × 4
2 355: indeed, 2 355 = 471 × 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 471). 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 21.703). 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 471

Preceding numbers: …469, 470
Following numbers: 472, 473…

Nearest numbers from 471

Preceding prime number: 467
Following prime number: 479