The number 2100
2100 is a composite number with 36 divisors. Its prime factorisation is × 3 × × 7. Divisors (36): 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30 … 2100.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 2100: a Harshad number: divisible by its digit sum 3.
- 2
2100 is composite. Its prime factorisation is
- 3
The divisors add up to 6944; without 2100 itself that is 4844, so 2100 is abundant (4844 is more than 2100). Euler's totient φ(2100) = 480 numbers up to 2100 share no factor with it.
- 4
The digits of 2100 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 32 steps to reach 1.
LaTeX source of the formulas on this page
\[ 2100 = 2^{2} \times 3 \times 5^{2} \times 7 \]2100 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 6944 |
| Euler totient φ(n) | 480 |
| Square | 4410000 |
| Cube | 9261000000 |
| Square root | 45.825757 (= 10√21) |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 32 |
| Scientific notation | 2.1 × |
2100 in other forms
| Form | Value |
|---|---|
| In words | two thousand one hundred |
| Roman numerals | MMC |
| Binary (base 2) | 100000110100 |
| Octal (base 8) | 4064 |
| Hexadecimal (base 16) | 834 |
| Base 3 | 2212210 |
| As time | 2100 seconds = 35 min 0 s |
Is 2100 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (2100 ÷ 2 = 1050) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (2100 ÷ 3 = 700) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (2100 ÷ 4 = 525) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (2100 ÷ 5 = 420) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (2100 ÷ 6 = 350) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (2100 ÷ 7 = 300) | 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 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (2100 ÷ 10 = 210) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (2100 ÷ 12 = 175) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 2100 a prime number?
No. 2100 = × 3 × × 7, so it is divisible by 2.
What are the factors of 2100?
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 2100.
What is 2100 in binary?
100000110100 (hexadecimal 834, octal 4064).
What is the square root of 2100?
About 45.8258, exactly 10√21.
What is 2100 in Roman numerals?
MMC.
Is 2100 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 2100?
2100 is a Harshad number: divisible by its digit sum 3.