The number 17920
17920 is a composite number with 40 divisors. Its prime factorisation is × 5 × 7. Divisors (40): 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64 … 17920.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
17920 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
17920 is composite. Its prime factorisation is
- 3
The divisors add up to 49104; without 17920 itself that is 31184, so 17920 is abundant (31184 is more than 17920). Euler's totient φ(17920) = 6144 numbers up to 17920 share no factor with it.
- 4
The digits of 17920 add up to 19, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 22 steps to reach 1.
LaTeX source of the formulas on this page
\[ 17920 = 2^{9} \times 5 \times 7 \]17920 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 49104 |
| Euler totient φ(n) | 6144 |
| Square | 321126400 |
| Cube | 5754585088000 |
| Square root | 133.865604 (= 16√70) |
| Digit sum / digital root | 19 / 1 |
| Collatz steps to 1 | 22 |
| Scientific notation | 1.792 × |
17920 in other forms
| Form | Value |
|---|---|
| In words | seventeen thousand nine hundred and twenty |
| Binary (base 2) | 100011000000000 |
| Octal (base 8) | 43000 |
| Hexadecimal (base 16) | 4600 |
| Base 3 | 220120201 |
| As time | 17920 seconds = 4 h 58 min 40 s |
Is 17920 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (17920 ÷ 2 = 8960) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (17920 ÷ 4 = 4480) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (17920 ÷ 5 = 3584) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (17920 ÷ 7 = 2560) | 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 (17920 ÷ 8 = 2240) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 1) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (17920 ÷ 10 = 1792) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 17920 a prime number?
No. 17920 = × 5 × 7, so it is divisible by 2.
What are the factors of 17920?
1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 128, 140, 160, 224, 256, 280, 320, 448, 512, 560, 640, 896, 1120, 1280, 1792, 2240, 2560, 3584, 4480, 8960, 17920.
What is 17920 in binary?
100011000000000 (hexadecimal 4600, octal 43000).
What is the square root of 17920?
About 133.8656, exactly 16√70.
Is 17920 divisible by 3?
No. Its digits add up to 19, which is not a multiple of 3.
What is special about the number 17920?
It is a composite number with 40 divisors.