Is 100 a prime number? What are the divisors of 100?

Is 100 a prime number?

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

For 100, the answer is: No, 100 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 100) is as follows: 1, 2, 4, 5, 10, 20, 25, 50, 100.

To be 100 a prime number, it would have been required that 100 has only two divisors, i.e., itself and 1.

As a consequence:

  • 100 is a multiple of 1
  • 100 is a multiple of 2
  • 100 is a multiple of 4
  • 100 is a multiple of 5
  • 100 is a multiple of 10
  • 100 is a multiple of 20
  • 100 is a multiple of 25
  • 100 is a multiple of 50

To be 100 a prime number, it would have been required that 100 has only two divisors, i.e., itself and 1.

Is 100 a deficient number?

No, 100 is not a deficient number: to be deficient, 100 should have been such that 100 is larger than the sum of its proper divisors, i.e., the divisors of 100 without 100 itself (that is 1 + 2 + 4 + 5 + 10 + 20 + 25 + 50 = 117).

In fact, 100 is an abundant number; 100 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 5 + 10 + 20 + 25 + 50 = 117). The smallest abundant number is 12.

Parity of 100

100 is an even number, because it is evenly divisible by 2: 100 / 2 = 50.

Is 100 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 100 is 10.

Therefore, the square root of 100 is an integer, and as a consequence 100 is a perfect square.

As a consequence, 10 is the square root of 100.

What is the square number of 100?

The square of a number (here 100) is the result of the product of this number (100) by itself (i.e., 100 × 100); the square of 100 is sometimes called "raising 100 to the power 2", or "100 squared".

The square of 100 is 10 000 because 100 × 100 = 1002 = 10 000.

As a consequence, 100 is the square root of 10 000.

Number of digits of 100

100 is a number with 3 digits.

What are the multiples of 100?

The multiples of 100 are all integers evenly divisible by 100, that is all numbers such that the remainder of the division by 100 is zero. There are infinitely many multiples of 100. The smallest multiples of 100 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 100 too, since 0 × 100 = 0
  • 100: indeed, 100 is a multiple of itself, since 100 is evenly divisible by 100 (we have 100 / 100 = 1, so the remainder of this division is indeed zero)
  • 200: indeed, 200 = 100 × 2
  • 300: indeed, 300 = 100 × 3
  • 400: indeed, 400 = 100 × 4
  • 500: indeed, 500 = 100 × 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 100). 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 10). 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 100

  • Preceding numbers: …98, 99
  • Following numbers: 101, 102

Nearest numbers from 100

  • Preceding prime number: 97
  • Following prime number: 101
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