Is 99 a prime number? What are the divisors of 99?

Is 99 a prime number?

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

For 99, the answer is: No, 99 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 99) is as follows: 1, 3, 9, 11, 33, 99.

To be 99 a prime number, it would have been required that 99 has only two divisors, i.e., itself and 1.

As a consequence:

  • 99 is a multiple of 1
  • 99 is a multiple of 3
  • 99 is a multiple of 9
  • 99 is a multiple of 11
  • 99 is a multiple of 33

To be 99 a prime number, it would have been required that 99 has only two divisors, i.e., itself and 1.

Is 99 a deficient number?

Yes, 99 is a deficient number, that is to say 99 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 99 without 99 itself (that is 1 + 3 + 9 + 11 + 33 = 57).

Parity of 99

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

Is 99 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 99 is about 9.950.

Thus, the square root of 99 is not an integer, and therefore 99 is not a square number.

What is the square number of 99?

The square of a number (here 99) is the result of the product of this number (99) by itself (i.e., 99 × 99); the square of 99 is sometimes called "raising 99 to the power 2", or "99 squared".

The square of 99 is 9 801 because 99 × 99 = 992 = 9 801.

As a consequence, 99 is the square root of 9 801.

Number of digits of 99

99 is a number with 2 digits.

What are the multiples of 99?

The multiples of 99 are all integers evenly divisible by 99, that is all numbers such that the remainder of the division by 99 is zero. There are infinitely many multiples of 99. The smallest multiples of 99 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 99 too, since 0 × 99 = 0
  • 99: indeed, 99 is a multiple of itself, since 99 is evenly divisible by 99 (we have 99 / 99 = 1, so the remainder of this division is indeed zero)
  • 198: indeed, 198 = 99 × 2
  • 297: indeed, 297 = 99 × 3
  • 396: indeed, 396 = 99 × 4
  • 495: indeed, 495 = 99 × 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 99). 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 9.950). 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 99

  • Preceding numbers: …97, 98
  • Following numbers: 100, 101

Nearest numbers from 99

  • Preceding prime number: 97
  • Following prime number: 101
Find out whether some integer is a prime number