Is 20 a prime number?

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

For 20, the answer is: No, 20 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 20) is as follows: 1, 2, 4, 5, 10, 20.

For 20 to be a prime number, it would have been required that 20 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 20 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 20 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

20 is a multiple of 1
20 is a multiple of 2
20 is a multiple of 4
20 is a multiple of 5
20 is a multiple of 10

For 20 to be a prime number, it would have been required that 20 has only two divisors, i.e., itself and 1.

Is 20 a deficient number?

No, 20 is not a deficient number: to be deficient, 20 should have been such that 20 is larger than the sum of its proper divisors, i.e., the divisors of 20 without 20 itself (that is 1 + 2 + 4 + 5 + 10 = 22).

In fact, 20 is an abundant number; 20 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 10 = 22). The smallest abundant number is 12.

Parity of 20

20 is an even number, because it is evenly divisible by 2: 20 / 2 = 10.

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What is an even number?

Is 20 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 20 is about 4.472.

Thus, the square root of 20 is not an integer, and therefore 20 is not a square number.

What is the square number of 20?

The square of a number (here 20) is the result of the product of this number (20) by itself (i.e., 20 × 20); the square of 20 is sometimes called "raising 20 to the power 2", or "20 squared".

The square of 20 is 400 because 20 × 20 = 20² = 400.

As a consequence, 20 is the square root of 400.

Number of digits of 20

20 is a number with 2 digits.

What are the multiples of 20?

The multiples of 20 are all integers evenly divisible by 20, that is all numbers such that the remainder of the division by 20 is zero. There are infinitely many multiples of 20. The smallest multiples of 20 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 20 too, since 0 × 20 = 0
20: indeed, 20 is a multiple of itself, since 20 is evenly divisible by 20 (we have 20 / 20 = 1, so the remainder of this division is indeed zero)
40: indeed, 40 = 20 × 2
60: indeed, 60 = 20 × 3
80: indeed, 80 = 20 × 4
100: indeed, 100 = 20 × 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 20). 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 4.472). 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 20

Preceding numbers: …18, 19
Following numbers: 21, 22…

Nearest numbers from 20

Preceding prime number: 19
Following prime number: 23