The number 71880
71880 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 599. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 … 71880.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 71880: a Harshad number: divisible by its digit sum 24.
- 2
71880 is composite. Its prime factorisation is
- 3
The divisors add up to 216000; without 71880 itself that is 144120, so 71880 is abundant (144120 is more than 71880). Euler's totient φ(71880) = 19136 numbers up to 71880 share no factor with it.
- 4
The digits of 71880 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 187 steps to reach 1.
LaTeX source of the formulas on this page
\[ 71880 = 2^{3} \times 3 \times 5 \times 599 \]71880 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 216000 |
| Euler totient φ(n) | 19136 |
| Square | 5166734400 |
| Cube | 371384868672000 |
| Square root | 268.104457 (= 2√17970) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 187 |
| Scientific notation | 7.188 × |
71880 in other forms
| Form | Value |
|---|---|
| In words | seventy-one thousand eight hundred and eighty |
| Binary (base 2) | 10001100011001000 |
| Octal (base 8) | 214310 |
| Hexadecimal (base 16) | 118C8 |
| Base 3 | 10122121020 |
| As time | 71880 seconds = 19 h 58 min 0 s |
Is 71880 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (71880 ÷ 2 = 35940) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (71880 ÷ 3 = 23960) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (71880 ÷ 4 = 17970) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (71880 ÷ 5 = 14376) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (71880 ÷ 6 = 11980) | 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 (71880 ÷ 8 = 8985) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (71880 ÷ 10 = 7188) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (71880 ÷ 12 = 5990) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 71880 a prime number?
No. 71880 = × 3 × 5 × 599, so it is divisible by 2.
What are the factors of 71880?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 599, 1198, 1797, 2396, 2995, 3594, 4792, 5990, 7188, 8985, 11980, 14376, 17970, 23960, 35940, 71880.
What is 71880 in binary?
10001100011001000 (hexadecimal 118C8, octal 214310).
What is the square root of 71880?
About 268.1045, exactly 2√17970.
Is 71880 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 71880?
71880 is a Harshad number: divisible by its digit sum 24.