Is 475 a prime number?

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

For 475, the answer is: No, 475 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 475) is as follows: 1, 5, 19, 25, 95, 475.

For 475 to be a prime number, it would have been required that 475 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 475 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 475 is 5, so it is divisible by 5 and is therefore not prime.

As a consequence:

475 is a multiple of 1
475 is a multiple of 5
475 is a multiple of 19
475 is a multiple of 25
475 is a multiple of 95

For 475 to be a prime number, it would have been required that 475 has only two divisors, i.e., itself and 1.

Is 475 a deficient number?

Yes, 475 is a deficient number, that is to say 475 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 475 without 475 itself (that is 1 + 5 + 19 + 25 + 95 = 145).

Parity of 475

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

Find out more:

What is an even number?

Is 475 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 475 is about 21.794.

Thus, the square root of 475 is not an integer, and therefore 475 is not a square number.

What is the square number of 475?

The square of a number (here 475) is the result of the product of this number (475) by itself (i.e., 475 × 475); the square of 475 is sometimes called "raising 475 to the power 2", or "475 squared".

The square of 475 is 225 625 because 475 × 475 = 475² = 225 625.

As a consequence, 475 is the square root of 225 625.

Number of digits of 475

475 is a number with 3 digits.

What are the multiples of 475?

The multiples of 475 are all integers evenly divisible by 475, that is all numbers such that the remainder of the division by 475 is zero. There are infinitely many multiples of 475. The smallest multiples of 475 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 475 too, since 0 × 475 = 0
475: indeed, 475 is a multiple of itself, since 475 is evenly divisible by 475 (we have 475 / 475 = 1, so the remainder of this division is indeed zero)
950: indeed, 950 = 475 × 2
1 425: indeed, 1 425 = 475 × 3
1 900: indeed, 1 900 = 475 × 4
2 375: indeed, 2 375 = 475 × 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 475). 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 21.794). 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 475

Preceding numbers: …473, 474
Following numbers: 476, 477…

Nearest numbers from 475

Preceding prime number: 467
Following prime number: 479