Is 470 a prime number?

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

For 470, the answer is: No, 470 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 470) is as follows: 1, 2, 5, 10, 47, 94, 235, 470.

For 470 to be a prime number, it would have been required that 470 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 470 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 470 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

470 is a multiple of 1
470 is a multiple of 2
470 is a multiple of 5
470 is a multiple of 10
470 is a multiple of 47
470 is a multiple of 94
470 is a multiple of 235

For 470 to be a prime number, it would have been required that 470 has only two divisors, i.e., itself and 1.

Is 470 a deficient number?

Yes, 470 is a deficient number, that is to say 470 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 470 without 470 itself (that is 1 + 2 + 5 + 10 + 47 + 94 + 235 = 394).

Parity of 470

470 is an even number, because it is evenly divisible by 2: 470 / 2 = 235.

Find out more:

What is an even number?

Is 470 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 470 is about 21.679.

Thus, the square root of 470 is not an integer, and therefore 470 is not a square number.

What is the square number of 470?

The square of a number (here 470) is the result of the product of this number (470) by itself (i.e., 470 × 470); the square of 470 is sometimes called "raising 470 to the power 2", or "470 squared".

The square of 470 is 220 900 because 470 × 470 = 470² = 220 900.

As a consequence, 470 is the square root of 220 900.

Number of digits of 470

470 is a number with 3 digits.

What are the multiples of 470?

The multiples of 470 are all integers evenly divisible by 470, that is all numbers such that the remainder of the division by 470 is zero. There are infinitely many multiples of 470. The smallest multiples of 470 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 470 too, since 0 × 470 = 0
470: indeed, 470 is a multiple of itself, since 470 is evenly divisible by 470 (we have 470 / 470 = 1, so the remainder of this division is indeed zero)
940: indeed, 940 = 470 × 2
1 410: indeed, 1 410 = 470 × 3
1 880: indeed, 1 880 = 470 × 4
2 350: indeed, 2 350 = 470 × 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 470). 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 21.679). 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 470

Preceding numbers: …468, 469
Following numbers: 471, 472…

Nearest numbers from 470

Preceding prime number: 467
Following prime number: 479