Is 21 a prime number? What are the divisors of 21?

Is 21 a prime number?

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

For 21, the answer is: No, 21 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 21) is as follows: 1, 3, 7, 21.

To be 21 a prime number, it would have been required that 21 has only two divisors, i.e., itself and 1.

As a consequence:

  • 21 is a multiple of 1
  • 21 is a multiple of 3
  • 21 is a multiple of 7

To be 21 a prime number, it would have been required that 21 has only two divisors, i.e., itself and 1.

However, 21 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 21 = 3 x 7, where 3 and 7 are both prime numbers.

Is 21 a deficient number?

Yes, 21 is a deficient number, that is to say 21 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 21 without 21 itself (that is 1 + 3 + 7 = 11).

Parity of 21

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

Is 21 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 21 is about 4.583.

Thus, the square root of 21 is not an integer, and therefore 21 is not a square number.

What is the square number of 21?

The square of a number (here 21) is the result of the product of this number (21) by itself (i.e., 21 × 21); the square of 21 is sometimes called "raising 21 to the power 2", or "21 squared".

The square of 21 is 441 because 21 × 21 = 212 = 441.

As a consequence, 21 is the square root of 441.

Number of digits of 21

21 is a number with 2 digits.

What are the multiples of 21?

The multiples of 21 are all integers evenly divisible by 21, that is all numbers such that the remainder of the division by 21 is zero. There are infinitely many multiples of 21. The smallest multiples of 21 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 21 too, since 0 × 21 = 0
  • 21: indeed, 21 is a multiple of itself, since 21 is evenly divisible by 21 (we have 21 / 21 = 1, so the remainder of this division is indeed zero)
  • 42: indeed, 42 = 21 × 2
  • 63: indeed, 63 = 21 × 3
  • 84: indeed, 84 = 21 × 4
  • 105: indeed, 105 = 21 × 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 21). 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 4.583). 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 21

  • Preceding numbers: …19, 20
  • Following numbers: 22, 23

Nearest numbers from 21

  • Preceding prime number: 19
  • Following prime number: 23
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