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.

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

Find out more:

What is a prime number?

Actually, one can immediately see that 900 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 900 is 0, so it is divisible by 5 and is therefore not prime.

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

For 900 to be 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.

Find out more:

What is an even number?

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