The number 8100
8100 is a perfect square (90²). Its prime factorisation is × × . Divisors (45): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36 … 8100.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 8100: a perfect square (90²); a Harshad number: divisible by its digit sum 9.
- 2
8100 is composite. Its prime factorisation is
- 3
The divisors add up to 26257; without 8100 itself that is 18157, so 8100 is abundant (18157 is more than 8100). Euler's totient φ(8100) = 2160 numbers up to 8100 share no factor with it.
- 4
The digits of 8100 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 158 steps to reach 1.
LaTeX source of the formulas on this page
\[ 8100 = 2^{2} \times 3^{4} \times 5^{2} \]8100 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 45 |
| Sum of divisors | 26257 |
| Euler totient φ(n) | 2160 |
| Square | 65610000 |
| Cube | 531441000000 |
| Square root | 90 |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 158 |
| Scientific notation | 8.1 × |
| Perfect power |
8100 in other forms
| Form | Value |
|---|---|
| In words | eight thousand one hundred |
| Binary (base 2) | 1111110100100 |
| Octal (base 8) | 17644 |
| Hexadecimal (base 16) | 1FA4 |
| Base 3 | 102010000 |
| As time | 8100 seconds = 2 h 15 min 0 s |
Is 8100 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (8100 ÷ 2 = 4050) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (8100 ÷ 3 = 2700) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (8100 ÷ 4 = 2025) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (8100 ÷ 5 = 1620) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (8100 ÷ 6 = 1350) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (8100 ÷ 9 = 900) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (8100 ÷ 10 = 810) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (8100 ÷ 12 = 675) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 8100 a prime number?
No. 8100 = × × , so it is divisible by 2.
What are the factors of 8100?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 36, 45, 50, 54, 60, 75, 81, 90, 100, 108, 135, 150, 162, 180, 225, 270, 300, 324, 405, 450, 540, 675, 810, 900, 1350, 1620, 2025, 2700, 4050, 8100.
What is 8100 in binary?
1111110100100 (hexadecimal 1FA4, octal 17644).
What is the square root of 8100?
90, because 90 × 90 = 8100.
Is 8100 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 8100?
8100 is a perfect square (90²); a Harshad number: divisible by its digit sum 9.