Is 627 a prime number?

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

For 627, the answer is: No, 627 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 627) is as follows: 1, 3, 11, 19, 33, 57, 209, 627.

For 627 to be a prime number, it would have been required that 627 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

627 is a multiple of 1
627 is a multiple of 3
627 is a multiple of 11
627 is a multiple of 19
627 is a multiple of 33
627 is a multiple of 57
627 is a multiple of 209

For 627 to be a prime number, it would have been required that 627 has only two divisors, i.e., itself and 1.

Is 627 a deficient number?

Yes, 627 is a deficient number, that is to say 627 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 627 without 627 itself (that is 1 + 3 + 11 + 19 + 33 + 57 + 209 = 333).

Parity of 627

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

Find out more:

What is an even number?

Is 627 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 627 is about 25.040.

Thus, the square root of 627 is not an integer, and therefore 627 is not a square number.

What is the square number of 627?

The square of a number (here 627) is the result of the product of this number (627) by itself (i.e., 627 × 627); the square of 627 is sometimes called "raising 627 to the power 2", or "627 squared".

The square of 627 is 393 129 because 627 × 627 = 627² = 393 129.

As a consequence, 627 is the square root of 393 129.

Number of digits of 627

627 is a number with 3 digits.

What are the multiples of 627?

The multiples of 627 are all integers evenly divisible by 627, that is all numbers such that the remainder of the division by 627 is zero. There are infinitely many multiples of 627. The smallest multiples of 627 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 627 too, since 0 × 627 = 0
627: indeed, 627 is a multiple of itself, since 627 is evenly divisible by 627 (we have 627 / 627 = 1, so the remainder of this division is indeed zero)
1 254: indeed, 1 254 = 627 × 2
1 881: indeed, 1 881 = 627 × 3
2 508: indeed, 2 508 = 627 × 4
3 135: indeed, 3 135 = 627 × 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 627). 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 25.040). 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 627

Preceding numbers: …625, 626
Following numbers: 628, 629…

Nearest numbers from 627

Preceding prime number: 619
Following prime number: 631