The number 21000
21000 is a composite number with 64 divisors. Its prime factorisation is × 3 × × 7. Divisors (64): 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25 … 21000.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 21000: a Harshad number: divisible by its digit sum 3.
- 2
21000 is composite. Its prime factorisation is
- 3
The divisors add up to 74880; without 21000 itself that is 53880, so 21000 is abundant (53880 is more than 21000). Euler's totient φ(21000) = 4800 numbers up to 21000 share no factor with it.
- 4
The digits of 21000 add up to 3, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 30 steps to reach 1.
LaTeX source of the formulas on this page
\[ 21000 = 2^{3} \times 3 \times 5^{3} \times 7 \]21000 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 64 |
| Sum of divisors | 74880 |
| Euler totient φ(n) | 4800 |
| Square | 441000000 |
| Cube | 9261000000000 |
| Square root | 144.913767 (= 10√210) |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 30 |
| Scientific notation | 2.1 × |
21000 in other forms
| Form | Value |
|---|---|
| In words | twenty-one thousand |
| Binary (base 2) | 101001000001000 |
| Octal (base 8) | 51010 |
| Hexadecimal (base 16) | 5208 |
| Base 3 | 1001210210 |
| As time | 21000 seconds = 5 h 50 min 0 s |
Is 21000 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (21000 ÷ 2 = 10500) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (21000 ÷ 3 = 7000) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (21000 ÷ 4 = 5250) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (21000 ÷ 5 = 4200) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (21000 ÷ 6 = 3500) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (21000 ÷ 7 = 3000) | 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 | Yes (21000 ÷ 8 = 2625) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (21000 ÷ 10 = 2100) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (21000 ÷ 12 = 1750) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 21000 a prime number?
No. 21000 = × 3 × × 7, so it is divisible by 2.
What are the factors of 21000?
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 25, 28, 30, 35, 40, 42, 50, 56, 60, 70, 75, 84, 100, 105, 120, 125, 140, 150, 168, 175, 200, 210, 250, 280, 300, 350, 375, 420, 500, 525, 600, 700, 750, 840, 875, 1000, 1050, 1400, 1500, 1750, 2100, 2625, 3000, 3500, 4200, 5250, 7000, 10500, 21000.
What is 21000 in binary?
101001000001000 (hexadecimal 5208, octal 51010).
What is the square root of 21000?
About 144.9138, exactly 10√210.
Is 21000 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 21000?
21000 is a Harshad number: divisible by its digit sum 3.