The number 900
900 is a perfect square (30²). Its prime factorisation is × × . Divisors (27): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45 … 900.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 900: a perfect square (30²); a Harshad number: divisible by its digit sum 9.
- 2
900 is composite. Its prime factorisation is
- 3
The divisors add up to 2821; without 900 itself that is 1921, so 900 is abundant (1921 is more than 900). Euler's totient φ(900) = 240 numbers up to 900 share no factor with it.
- 4
The digits of 900 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 900 = 2^{2} \times 3^{2} \times 5^{2} \]900 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 27 |
| Sum of divisors | 2821 |
| Euler totient φ(n) | 240 |
| Square | 810000 |
| Cube | 729000000 |
| Square root | 30 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 54 |
| Scientific notation | 9 × |
| Perfect power |
900 in other forms
| Form | Value |
|---|---|
| In words | nine hundred |
| Roman numerals | CM |
| Binary (base 2) | 1110000100 |
| Octal (base 8) | 1604 |
| Hexadecimal (base 16) | 384 |
| Base 3 | 1020100 |
| As time | 900 seconds = 15 min 0 s |
Is 900 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (900 ÷ 2 = 450) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (900 ÷ 3 = 300) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (900 ÷ 4 = 225) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (900 ÷ 5 = 180) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (900 ÷ 6 = 150) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (900 ÷ 9 = 100) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (900 ÷ 10 = 90) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (900 ÷ 12 = 75) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 900 a prime number?
No. 900 = × × , so it is divisible by 2.
What are the factors of 900?
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.
What is 900 in binary?
1110000100 (hexadecimal 384, octal 1604).
What is the square root of 900?
30, because 30 × 30 = 900.
What is 900 in Roman numerals?
CM.
Is 900 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 900?
900 is a perfect square (30²); a Harshad number: divisible by its digit sum 9.