The number 72720
72720 is a composite number with 60 divisors. Its prime factorisation is × × 5 × 101. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 72720.
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How to work it out
- 1
What is special about 72720: a Harshad number: divisible by its digit sum 18.
- 2
72720 is composite. Its prime factorisation is
- 3
The divisors add up to 246636; without 72720 itself that is 173916, so 72720 is abundant (173916 is more than 72720). Euler's totient φ(72720) = 19200 numbers up to 72720 share no factor with it.
- 4
The digits of 72720 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 143 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72720 = 2^{4} \times 3^{2} \times 5 \times 101 \]72720 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 246636 |
| Euler totient φ(n) | 19200 |
| Square | 5288198400 |
| Cube | 384557787648000 |
| Square root | 269.666461 (= 12√505) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 143 |
| Scientific notation | 7.272 × |
72720 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand seven hundred and twenty |
| Binary (base 2) | 10001110000010000 |
| Octal (base 8) | 216020 |
| Hexadecimal (base 16) | 11C10 |
| Base 3 | 10200202100 |
| As time | 72720 seconds = 20 h 12 min 0 s |
Is 72720 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72720 ÷ 2 = 36360) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72720 ÷ 3 = 24240) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72720 ÷ 4 = 18180) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (72720 ÷ 5 = 14544) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (72720 ÷ 6 = 12120) | 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 | Yes (72720 ÷ 8 = 9090) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (72720 ÷ 9 = 8080) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (72720 ÷ 10 = 7272) | 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 (72720 ÷ 12 = 6060) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72720 a prime number?
No. 72720 = × × 5 × 101, so it is divisible by 2.
What are the factors of 72720?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 101, 120, 144, 180, 202, 240, 303, 360, 404, 505, 606, 720, 808, 909, 1010, 1212, 1515, 1616, 1818, 2020, 2424, 3030, 3636, 4040, 4545, 4848, 6060, 7272, 8080, 9090, 12120, 14544, 18180, 24240, 36360, 72720.
What is 72720 in binary?
10001110000010000 (hexadecimal 11C10, octal 216020).
What is the square root of 72720?
About 269.6665, exactly 12√505.
Is 72720 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 72720?
72720 is a Harshad number: divisible by its digit sum 18.