Is 644 a prime number?

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

For 644, the answer is: No, 644 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 644) is as follows: 1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644.

For 644 to be a prime number, it would have been required that 644 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

644 is a multiple of 1
644 is a multiple of 2
644 is a multiple of 4
644 is a multiple of 7
644 is a multiple of 14
644 is a multiple of 23
644 is a multiple of 28
644 is a multiple of 46
644 is a multiple of 92
644 is a multiple of 161
644 is a multiple of 322

For 644 to be a prime number, it would have been required that 644 has only two divisors, i.e., itself and 1.

Is 644 a deficient number?

No, 644 is not a deficient number: to be deficient, 644 should have been such that 644 is larger than the sum of its proper divisors, i.e., the divisors of 644 without 644 itself (that is 1 + 2 + 4 + 7 + 14 + 23 + 28 + 46 + 92 + 161 + 322 = 700).

In fact, 644 is an abundant number; 644 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 7 + 14 + 23 + 28 + 46 + 92 + 161 + 322 = 700). The smallest abundant number is 12.

Parity of 644

644 is an even number, because it is evenly divisible by 2: 644 / 2 = 322.

Find out more:

What is an even number?

Is 644 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 644 is about 25.377.

Thus, the square root of 644 is not an integer, and therefore 644 is not a square number.

What is the square number of 644?

The square of a number (here 644) is the result of the product of this number (644) by itself (i.e., 644 × 644); the square of 644 is sometimes called "raising 644 to the power 2", or "644 squared".

The square of 644 is 414 736 because 644 × 644 = 644² = 414 736.

As a consequence, 644 is the square root of 414 736.

Number of digits of 644

644 is a number with 3 digits.

What are the multiples of 644?

The multiples of 644 are all integers evenly divisible by 644, that is all numbers such that the remainder of the division by 644 is zero. There are infinitely many multiples of 644. The smallest multiples of 644 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 644 too, since 0 × 644 = 0
644: indeed, 644 is a multiple of itself, since 644 is evenly divisible by 644 (we have 644 / 644 = 1, so the remainder of this division is indeed zero)
1 288: indeed, 1 288 = 644 × 2
1 932: indeed, 1 932 = 644 × 3
2 576: indeed, 2 576 = 644 × 4
3 220: indeed, 3 220 = 644 × 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 644). 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 25.377). 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 644

Preceding numbers: …642, 643
Following numbers: 645, 646…

Nearest numbers from 644

Preceding prime number: 643
Following prime number: 647