Is 637 a prime number?

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

For 637, the answer is: No, 637 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 637) is as follows: 1, 7, 13, 49, 91, 637.

For 637 to be a prime number, it would have been required that 637 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

637 is a multiple of 1
637 is a multiple of 7
637 is a multiple of 13
637 is a multiple of 49
637 is a multiple of 91

For 637 to be a prime number, it would have been required that 637 has only two divisors, i.e., itself and 1.

Is 637 a deficient number?

Yes, 637 is a deficient number, that is to say 637 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 637 without 637 itself (that is 1 + 7 + 13 + 49 + 91 = 161).

Parity of 637

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

Find out more:

What is an even number?

Is 637 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 637 is about 25.239.

Thus, the square root of 637 is not an integer, and therefore 637 is not a square number.

What is the square number of 637?

The square of a number (here 637) is the result of the product of this number (637) by itself (i.e., 637 × 637); the square of 637 is sometimes called "raising 637 to the power 2", or "637 squared".

The square of 637 is 405 769 because 637 × 637 = 637² = 405 769.

As a consequence, 637 is the square root of 405 769.

Number of digits of 637

637 is a number with 3 digits.

What are the multiples of 637?

The multiples of 637 are all integers evenly divisible by 637, that is all numbers such that the remainder of the division by 637 is zero. There are infinitely many multiples of 637. The smallest multiples of 637 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 637 too, since 0 × 637 = 0
637: indeed, 637 is a multiple of itself, since 637 is evenly divisible by 637 (we have 637 / 637 = 1, so the remainder of this division is indeed zero)
1 274: indeed, 1 274 = 637 × 2
1 911: indeed, 1 911 = 637 × 3
2 548: indeed, 2 548 = 637 × 4
3 185: indeed, 3 185 = 637 × 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 637). 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 25.239). 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 637

Preceding numbers: …635, 636
Following numbers: 638, 639…

Nearest numbers from 637

Preceding prime number: 631
Following prime number: 641