Is 12 a prime number? What are the divisors of 12?

Is 12 a prime number?

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

For 12, the answer is: No, 12 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 12) is as follows: 1, 2, 3, 4, 6, 12.

To be 12 a prime number, it would have been required that 12 has only two divisors, i.e., itself and 1.

As a consequence:

  • 12 is a multiple of 1
  • 12 is a multiple of 2
  • 12 is a multiple of 3
  • 12 is a multiple of 4
  • 12 is a multiple of 6

To be 12 a prime number, it would have been required that 12 has only two divisors, i.e., itself and 1.

Is 12 a deficient number?

No, 12 is not a deficient number: to be deficient, 12 should have been such that 12 is larger than the sum of its proper divisors, i.e., the divisors of 12 without 12 itself (that is 1 + 2 + 3 + 4 + 6 = 16).

In fact, 12 is an abundant number; 12 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 = 16). 12 is the smallest abundant number! The next abundant numbers are 18, 20, 24, 30… There are infinitely many abundant numbers.

Parity of 12

12 is an even number, because it is evenly divisible by 2: 12 / 2 = 6.

Is 12 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 12 is about 3.464.

Thus, the square root of 12 is not an integer, and therefore 12 is not a square number.

What is the square number of 12?

The square of a number (here 12) is the result of the product of this number (12) by itself (i.e., 12 × 12); the square of 12 is sometimes called "raising 12 to the power 2", or "12 squared".

The square of 12 is 144 because 12 × 12 = 122 = 144.

As a consequence, 12 is the square root of 144.

Number of digits of 12

12 is a number with 2 digits.

What are the multiples of 12?

The multiples of 12 are all integers evenly divisible by 12, that is all numbers such that the remainder of the division by 12 is zero. There are infinitely many multiples of 12. The smallest multiples of 12 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 12 too, since 0 × 12 = 0
  • 12: indeed, 12 is a multiple of itself, since 12 is evenly divisible by 12 (we have 12 / 12 = 1, so the remainder of this division is indeed zero)
  • 24: indeed, 24 = 12 × 2
  • 36: indeed, 36 = 12 × 3
  • 48: indeed, 48 = 12 × 4
  • 60: indeed, 60 = 12 × 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 12). 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 3.464). 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 12

  • Preceding numbers: …10, 11
  • Following numbers: 13, 14

Nearest numbers from 12

  • Preceding prime number: 11
  • Following prime number: 13
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