The number 12720
12720 is a triangular number: 1 + 2 + … + 159 = 12720. Its prime factorisation is × 3 × 5 × 53. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 12720.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 12720: a triangular number: 1 + 2 + … + 159 = 12720; a Harshad number: divisible by its digit sum 12.
- 2
12720 is composite. Its prime factorisation is
- 3
The divisors add up to 40176; without 12720 itself that is 27456, so 12720 is abundant (27456 is more than 12720). Euler's totient φ(12720) = 3328 numbers up to 12720 share no factor with it.
- 4
The digits of 12720 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 12720 = 2^{4} \times 3 \times 5 \times 53 \]12720 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 40176 |
| Euler totient φ(n) | 3328 |
| Square | 161798400 |
| Cube | 2058075648000 |
| Square root | 112.782977 (= 4√795) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 107 |
| Scientific notation | 1.272 × |
12720 in other forms
| Form | Value |
|---|---|
| In words | twelve thousand seven hundred and twenty |
| Binary (base 2) | 11000110110000 |
| Octal (base 8) | 30660 |
| Hexadecimal (base 16) | 31B0 |
| Base 3 | 122110010 |
| As time | 12720 seconds = 3 h 32 min 0 s |
Is 12720 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (12720 ÷ 2 = 6360) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (12720 ÷ 3 = 4240) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (12720 ÷ 4 = 3180) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (12720 ÷ 5 = 2544) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (12720 ÷ 6 = 2120) | 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 | Yes (12720 ÷ 8 = 1590) | 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 (12720 ÷ 10 = 1272) | 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 (12720 ÷ 12 = 1060) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 12720 a prime number?
No. 12720 = × 3 × 5 × 53, so it is divisible by 2.
What are the factors of 12720?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 53, 60, 80, 106, 120, 159, 212, 240, 265, 318, 424, 530, 636, 795, 848, 1060, 1272, 1590, 2120, 2544, 3180, 4240, 6360, 12720.
What is 12720 in binary?
11000110110000 (hexadecimal 31B0, octal 30660).
What is the square root of 12720?
About 112.7830, exactly 4√795.
Is 12720 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 12720?
12720 is a triangular number: 1 + 2 + … + 159 = 12720; a Harshad number: divisible by its digit sum 12.