The number 1215
1215 is a composite number with 12 divisors. Its prime factorisation is × 5. Divisors (12): 1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1215: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.
- 2
1215 is composite. Its prime factorisation is
- 3
The divisors add up to 2184; without 1215 itself that is 969, so 1215 is deficient (969 is less than 1215). Euler's totient φ(1215) = 648 numbers up to 1215 share no factor with it.
- 4
The digits of 1215 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 163 steps to reach 1.
LaTeX source of the formulas on this page
\[ 1215 = 3^{5} \times 5 \]1215 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 2184 |
| Euler totient φ(n) | 648 |
| Square | 1476225 |
| Cube | 1793613375 |
| Square root | 34.856850 (= 9√15) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 163 |
| Scientific notation | 1.215 × |
1215 in other forms
| Form | Value |
|---|---|
| In words | one thousand two hundred and fifteen |
| Roman numerals | MCCXV |
| Binary (base 2) | 10010111111 |
| Octal (base 8) | 2277 |
| Hexadecimal (base 16) | 4BF |
| Base 3 | 1200000 |
| As time | 1215 seconds = 20 min 15 s |
Is 1215 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (1215 ÷ 3 = 405) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 3) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (1215 ÷ 5 = 243) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (1215 ÷ 9 = 135) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 5) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 3) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1215 a prime number?
No. 1215 = × 5, so it is divisible by 3.
What are the factors of 1215?
1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 1215.
What is 1215 in binary?
10010111111 (hexadecimal 4BF, octal 2277).
What is the square root of 1215?
About 34.8569, exactly 9√15.
What is 1215 in Roman numerals?
MCCXV.
Is 1215 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 1215?
1215 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 9.