The number 20880
20880 is a composite number with 60 divisors. Its prime factorisation is × × 5 × 29. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 29 … 20880.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 20880: a Harshad number: divisible by its digit sum 18.
- 2
20880 is composite. Its prime factorisation is
- 3
The divisors add up to 72540; without 20880 itself that is 51660, so 20880 is abundant (51660 is more than 20880). Euler's totient φ(20880) = 5376 numbers up to 20880 share no factor with it.
- 4
The digits of 20880 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 56 steps to reach 1.
LaTeX source of the formulas on this page
\[ 20880 = 2^{4} \times 3^{2} \times 5 \times 29 \]20880 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 72540 |
| Euler totient φ(n) | 5376 |
| Square | 435974400 |
| Cube | 9103145472000 |
| Square root | 144.499135 (= 12√145) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 56 |
| Scientific notation | 2.088 × |
20880 in other forms
| Form | Value |
|---|---|
| In words | twenty thousand eight hundred and eighty |
| Binary (base 2) | 101000110010000 |
| Octal (base 8) | 50620 |
| Hexadecimal (base 16) | 5190 |
| Base 3 | 1001122100 |
| As time | 20880 seconds = 5 h 48 min 0 s |
Is 20880 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (20880 ÷ 2 = 10440) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (20880 ÷ 3 = 6960) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (20880 ÷ 4 = 5220) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (20880 ÷ 5 = 4176) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (20880 ÷ 6 = 3480) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (20880 ÷ 8 = 2610) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (20880 ÷ 9 = 2320) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (20880 ÷ 10 = 2088) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (20880 ÷ 12 = 1740) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 20880 a prime number?
No. 20880 = × × 5 × 29, so it is divisible by 2.
What are the factors of 20880?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 29, 30, 36, 40, 45, 48, 58, 60, 72, 80, 87, 90, 116, 120, 144, 145, 174, 180, 232, 240, 261, 290, 348, 360, 435, 464, 522, 580, 696, 720, 870, 1044, 1160, 1305, 1392, 1740, 2088, 2320, 2610, 3480, 4176, 5220, 6960, 10440, 20880.
What is 20880 in binary?
101000110010000 (hexadecimal 5190, octal 50620).
What is the square root of 20880?
About 144.4991, exactly 12√145.
Is 20880 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 20880?
20880 is a Harshad number: divisible by its digit sum 18.