The number 210
210 is a triangular number: 1 + 2 + … + 20 = 210. Its prime factorisation is 2 × 3 × 5 × 7. Divisors (16): 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 210: a triangular number: 1 + 2 + … + 20 = 210; a Harshad number: divisible by its digit sum 3.
- 2
210 is composite. Its prime factorisation is
- 3
The divisors add up to 576; without 210 itself that is 366, so 210 is abundant (366 is more than 210). Euler's totient φ(210) = 48 numbers up to 210 share no factor with it.
- 4
The digits of 210 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 39 steps to reach 1.
LaTeX source of the formulas on this page
\[ 210 = 2 \times 3 \times 5 \times 7 \]
210 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 576 |
| Euler totient φ(n) | 48 |
| Square | 44100 |
| Cube | 9261000 |
| Square root | 14.491377 |
| Digit sum / digital root | 3 / 3 |
| Collatz steps to 1 | 39 |
| Scientific notation | 2.1 × |
210 in other forms
| Form | Value |
|---|---|
| In words | two hundred and ten |
| Roman numerals | CCX |
| Binary (base 2) | 11010010 |
| Octal (base 8) | 322 |
| Hexadecimal (base 16) | D2 |
| Base 3 | 21210 |
| As time | 210 seconds = 3 min 30 s |
Is 210 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (210 ÷ 2 = 105) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (210 ÷ 3 = 70) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (210 ÷ 5 = 42) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (210 ÷ 6 = 35) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (210 ÷ 7 = 30) | 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 2) | 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 (210 ÷ 10 = 21) | 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 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 210 a prime number?
No. 210 = 2 × 3 × 5 × 7, so it is divisible by 2.
What are the factors of 210?
1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210.
What is 210 in binary?
11010010 (hexadecimal D2, octal 322).
What is the square root of 210?
About 14.4914.
What is 210 in Roman numerals?
CCX.
Is 210 divisible by 3?
Yes. Its digits add up to 3, a multiple of 3.
What is special about the number 210?
210 is a triangular number: 1 + 2 + … + 20 = 210; a Harshad number: divisible by its digit sum 3.