Is 28 a prime number? What are the divisors of 28?

Is 28 a prime number?

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

For 28, the answer is: No, 28 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 28) is as follows: 1, 2, 4, 7, 14, 28.

To be 28 a prime number, it would have been required that 28 has only two divisors, i.e., itself and 1.

As a consequence:

  • 28 is a multiple of 1
  • 28 is a multiple of 2
  • 28 is a multiple of 4
  • 28 is a multiple of 7
  • 28 is a multiple of 14

To be 28 a prime number, it would have been required that 28 has only two divisors, i.e., itself and 1.

Is 28 a deficient number?

No, 28 is not a deficient number: to be deficient, 28 should have been such that 28 is larger than the sum of its proper divisors, i.e., the divisors of 28 without 28 itself (that is 1 + 2 + 4 + 7 + 14 = 28).

Is 28 a perfect number?

Yes, 28 is a perfect number, that is to day 28 equals the sum of its proper positive divisors, i.e., the sum of its divisors excluding 28 itself.

Indeed, 28 = 1 + 2 + 4 + 7 + 14.

Note that perfect numbers are very rare: there are only 4 perfect numbers smaller than 1 000 000, viz., 6, 28, 496 and 8 128. Then, the next perfect number is already 33 550 336!

Parity of 28

28 is an even number, because it is evenly divisible by 2: 28 / 2 = 14.

Is 28 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 28 is about 5.292.

Thus, the square root of 28 is not an integer, and therefore 28 is not a square number.

What is the square number of 28?

The square of a number (here 28) is the result of the product of this number (28) by itself (i.e., 28 × 28); the square of 28 is sometimes called "raising 28 to the power 2", or "28 squared".

The square of 28 is 784 because 28 × 28 = 282 = 784.

As a consequence, 28 is the square root of 784.

Number of digits of 28

28 is a number with 2 digits.

What are the multiples of 28?

The multiples of 28 are all integers evenly divisible by 28, that is all numbers such that the remainder of the division by 28 is zero. There are infinitely many multiples of 28. The smallest multiples of 28 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 28 too, since 0 × 28 = 0
  • 28: indeed, 28 is a multiple of itself, since 28 is evenly divisible by 28 (we have 28 / 28 = 1, so the remainder of this division is indeed zero)
  • 56: indeed, 56 = 28 × 2
  • 84: indeed, 84 = 28 × 3
  • 112: indeed, 112 = 28 × 4
  • 140: indeed, 140 = 28 × 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 28). 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 5.292). 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 28

  • Preceding numbers: …26, 27
  • Following numbers: 29, 30

Nearest numbers from 28

  • Preceding prime number: 23
  • Following prime number: 29
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