Is 900 a prime number? What are the divisors of 900?

Is 900 a prime number?

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

For 900, the answer is: No, 900 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 900) is as follows: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900.

To be 900 a prime number, it would have been required that 900 has only two divisors, i.e., itself and 1.

As a consequence:

  • 900 is a multiple of 1
  • 900 is a multiple of 2
  • 900 is a multiple of 3
  • 900 is a multiple of 4
  • 900 is a multiple of 5
  • 900 is a multiple of 6
  • 900 is a multiple of 9
  • 900 is a multiple of 10
  • 900 is a multiple of 12
  • 900 is a multiple of 15
  • 900 is a multiple of 18
  • 900 is a multiple of 20
  • 900 is a multiple of 25
  • 900 is a multiple of 30
  • 900 is a multiple of 36
  • 900 is a multiple of 45
  • 900 is a multiple of 50
  • 900 is a multiple of 60
  • 900 is a multiple of 75
  • 900 is a multiple of 90
  • 900 is a multiple of 100
  • 900 is a multiple of 150
  • 900 is a multiple of 180
  • 900 is a multiple of 225
  • 900 is a multiple of 300
  • 900 is a multiple of 450

To be 900 a prime number, it would have been required that 900 has only two divisors, i.e., itself and 1.

Is 900 a deficient number?

No, 900 is not a deficient number: to be deficient, 900 should have been such that 900 is larger than the sum of its proper divisors, i.e., the divisors of 900 without 900 itself (that is 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 25 + 30 + 36 + 45 + 50 + 60 + 75 + 90 + 100 + 150 + 180 + 225 + 300 + 450 = 1 921).

In fact, 900 is an abundant number; 900 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 25 + 30 + 36 + 45 + 50 + 60 + 75 + 90 + 100 + 150 + 180 + 225 + 300 + 450 = 1 921). The smallest abundant number is 12.

Parity of 900

900 is an even number, because it is evenly divisible by 2: 900 / 2 = 450.

Is 900 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 900 is 30.

Therefore, the square root of 900 is an integer, and as a consequence 900 is a perfect square.

As a consequence, 30 is the square root of 900.

What is the square number of 900?

The square of a number (here 900) is the result of the product of this number (900) by itself (i.e., 900 × 900); the square of 900 is sometimes called "raising 900 to the power 2", or "900 squared".

The square of 900 is 810 000 because 900 × 900 = 9002 = 810 000.

As a consequence, 900 is the square root of 810 000.

Number of digits of 900

900 is a number with 3 digits.

What are the multiples of 900?

The multiples of 900 are all integers evenly divisible by 900, that is all numbers such that the remainder of the division by 900 is zero. There are infinitely many multiples of 900. The smallest multiples of 900 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 900 too, since 0 × 900 = 0
  • 900: indeed, 900 is a multiple of itself, since 900 is evenly divisible by 900 (we have 900 / 900 = 1, so the remainder of this division is indeed zero)
  • 1 800: indeed, 1 800 = 900 × 2
  • 2 700: indeed, 2 700 = 900 × 3
  • 3 600: indeed, 3 600 = 900 × 4
  • 4 500: indeed, 4 500 = 900 × 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 900). 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 30). 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 900

  • Preceding numbers: …898, 899
  • Following numbers: 901, 902

Nearest numbers from 900

  • Preceding prime number: 887
  • Following prime number: 907
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