Is 16 a prime number? What are the divisors of 16?

Is 16 a prime number?

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

For 16, the answer is: No, 16 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 16) is as follows: 1, 2, 4, 8, 16.

To be 16 a prime number, it would have been required that 16 has only two divisors, i.e., itself and 1.

As a consequence:

  • 16 is a multiple of 1
  • 16 is a multiple of 2
  • 16 is a multiple of 4
  • 16 is a multiple of 8

To be 16 a prime number, it would have been required that 16 has only two divisors, i.e., itself and 1.

Is 16 a deficient number?

Yes, 16 is a deficient number, that is to say 16 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 16 without 16 itself (that is 1 + 2 + 4 + 8 = 15).

Parity of 16

16 is an even number, because it is evenly divisible by 2: 16 / 2 = 8.

Is 16 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 16 is 4.

Therefore, the square root of 16 is an integer, and as a consequence 16 is a perfect square.

As a consequence, 4 is the square root of 16.

What is the square number of 16?

The square of a number (here 16) is the result of the product of this number (16) by itself (i.e., 16 × 16); the square of 16 is sometimes called "raising 16 to the power 2", or "16 squared".

The square of 16 is 256 because 16 × 16 = 162 = 256.

As a consequence, 16 is the square root of 256.

Number of digits of 16

16 is a number with 2 digits.

What are the multiples of 16?

The multiples of 16 are all integers evenly divisible by 16, that is all numbers such that the remainder of the division by 16 is zero. There are infinitely many multiples of 16. The smallest multiples of 16 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 16 too, since 0 × 16 = 0
  • 16: indeed, 16 is a multiple of itself, since 16 is evenly divisible by 16 (we have 16 / 16 = 1, so the remainder of this division is indeed zero)
  • 32: indeed, 32 = 16 × 2
  • 48: indeed, 48 = 16 × 3
  • 64: indeed, 64 = 16 × 4
  • 80: indeed, 80 = 16 × 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 16). 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 4). 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 16

  • Preceding numbers: …14, 15
  • Following numbers: 17, 18

Nearest numbers from 16

  • Preceding prime number: 13
  • Following prime number: 17
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