The number 72180
72180 is a composite number with 36 divisors. Its prime factorisation is × × 5 × 401. Divisors (36): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60 … 72180.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 72180: a Harshad number: divisible by its digit sum 18.
- 2
72180 is composite. Its prime factorisation is
- 3
The divisors add up to 219492; without 72180 itself that is 147312, so 72180 is abundant (147312 is more than 72180). Euler's totient φ(72180) = 19200 numbers up to 72180 share no factor with it.
- 4
The digits of 72180 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 156 steps to reach 1.
LaTeX source of the formulas on this page
\[ 72180 = 2^{2} \times 3^{2} \times 5 \times 401 \]72180 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 219492 |
| Euler totient φ(n) | 19200 |
| Square | 5209952400 |
| Cube | 376054364232000 |
| Square root | 268.663358 (= 6√2005) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 156 |
| Scientific notation | 7.218 × |
72180 in other forms
| Form | Value |
|---|---|
| In words | seventy-two thousand one hundred and eighty |
| Binary (base 2) | 10001100111110100 |
| Octal (base 8) | 214764 |
| Hexadecimal (base 16) | 119F4 |
| Base 3 | 10200000100 |
| As time | 72180 seconds = 20 h 3 min 0 s |
Is 72180 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (72180 ÷ 2 = 36090) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (72180 ÷ 3 = 24060) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (72180 ÷ 4 = 18045) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (72180 ÷ 5 = 14436) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (72180 ÷ 6 = 12030) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 | Yes (72180 ÷ 9 = 8020) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (72180 ÷ 10 = 7218) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (72180 ÷ 12 = 6015) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 72180 a prime number?
No. 72180 = × × 5 × 401, so it is divisible by 2.
What are the factors of 72180?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 401, 802, 1203, 1604, 2005, 2406, 3609, 4010, 4812, 6015, 7218, 8020, 12030, 14436, 18045, 24060, 36090, 72180.
What is 72180 in binary?
10001100111110100 (hexadecimal 119F4, octal 214764).
What is the square root of 72180?
About 268.6634, exactly 6√2005.
Is 72180 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 72180?
72180 is a Harshad number: divisible by its digit sum 18.