Is 640 a prime number?

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

For 640, the answer is: No, 640 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 640) is as follows: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 320, 640.

For 640 to be a prime number, it would have been required that 640 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 640 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 640 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

640 is a multiple of 1
640 is a multiple of 2
640 is a multiple of 4
640 is a multiple of 5
640 is a multiple of 8
640 is a multiple of 10
640 is a multiple of 16
640 is a multiple of 20
640 is a multiple of 32
640 is a multiple of 40
640 is a multiple of 64
640 is a multiple of 80
640 is a multiple of 128
640 is a multiple of 160
640 is a multiple of 320

For 640 to be a prime number, it would have been required that 640 has only two divisors, i.e., itself and 1.

Is 640 a deficient number?

No, 640 is not a deficient number: to be deficient, 640 should have been such that 640 is larger than the sum of its proper divisors, i.e., the divisors of 640 without 640 itself (that is 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 32 + 40 + 64 + 80 + 128 + 160 + 320 = 890).

In fact, 640 is an abundant number; 640 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 32 + 40 + 64 + 80 + 128 + 160 + 320 = 890). The smallest abundant number is 12.

Parity of 640

640 is an even number, because it is evenly divisible by 2: 640 / 2 = 320.

Find out more:

What is an even number?

Is 640 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 640 is about 25.298.

Thus, the square root of 640 is not an integer, and therefore 640 is not a square number.

What is the square number of 640?

The square of a number (here 640) is the result of the product of this number (640) by itself (i.e., 640 × 640); the square of 640 is sometimes called "raising 640 to the power 2", or "640 squared".

The square of 640 is 409 600 because 640 × 640 = 640² = 409 600.

As a consequence, 640 is the square root of 409 600.

Number of digits of 640

640 is a number with 3 digits.

What are the multiples of 640?

The multiples of 640 are all integers evenly divisible by 640, that is all numbers such that the remainder of the division by 640 is zero. There are infinitely many multiples of 640. The smallest multiples of 640 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 640 too, since 0 × 640 = 0
640: indeed, 640 is a multiple of itself, since 640 is evenly divisible by 640 (we have 640 / 640 = 1, so the remainder of this division is indeed zero)
1 280: indeed, 1 280 = 640 × 2
1 920: indeed, 1 920 = 640 × 3
2 560: indeed, 2 560 = 640 × 4
3 200: indeed, 3 200 = 640 × 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 640). 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 25.298). 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 640

Preceding numbers: …638, 639
Following numbers: 641, 642…

Nearest numbers from 640

Preceding prime number: 631
Following prime number: 641