Is 642 a prime number? What are the divisors of 642?

## Is 642 a prime number?

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

For 642, the answer is: No, 642 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 642) is as follows: 1, 2, 3, 6, 107, 214, 321, 642.

To be 642 a prime number, it would have been required that 642 has only two divisors, i.e., itself and 1.

As a consequence:

• 642 is a multiple of 1
• 642 is a multiple of 2
• 642 is a multiple of 3
• 642 is a multiple of 6
• 642 is a multiple of 107
• 642 is a multiple of 214
• 642 is a multiple of 321

To be 642 a prime number, it would have been required that 642 has only two divisors, i.e., itself and 1.

## Is 642 a deficient number?

No, 642 is not a deficient number: to be deficient, 642 should have been such that 642 is larger than the sum of its proper divisors, i.e., the divisors of 642 without 642 itself (that is 1 + 2 + 3 + 6 + 107 + 214 + 321 = 654).

In fact, 642 is an abundant number; 642 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 107 + 214 + 321 = 654). The smallest abundant number is 12.

## Parity of 642

642 is an even number, because it is evenly divisible by 2: 642 / 2 = 321.

## Is 642 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 642 is about 25.338.

Thus, the square root of 642 is not an integer, and therefore 642 is not a square number.

## What is the square number of 642?

The square of a number (here 642) is the result of the product of this number (642) by itself (i.e., 642 × 642); the square of 642 is sometimes called "raising 642 to the power 2", or "642 squared".

The square of 642 is 412 164 because 642 × 642 = 6422 = 412 164.

As a consequence, 642 is the square root of 412 164.

## Number of digits of 642

642 is a number with 3 digits.

## What are the multiples of 642?

The multiples of 642 are all integers evenly divisible by 642, that is all numbers such that the remainder of the division by 642 is zero. There are infinitely many multiples of 642. The smallest multiples of 642 are:

• 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 642 too, since 0 × 642 = 0
• 642: indeed, 642 is a multiple of itself, since 642 is evenly divisible by 642 (we have 642 / 642 = 1, so the remainder of this division is indeed zero)
• 1 284: indeed, 1 284 = 642 × 2
• 1 926: indeed, 1 926 = 642 × 3
• 2 568: indeed, 2 568 = 642 × 4
• 3 210: indeed, 3 210 = 642 × 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 642). 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 25.338). 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 642

• Preceding numbers: …640, 641
• Following numbers: 643, 644

## Nearest numbers from 642

• Preceding prime number: 641
• Following prime number: 643
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