The number 67920
67920 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 283. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 67920.
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How to work it out
- 1
What is special about 67920: a Harshad number: divisible by its digit sum 24.
- 2
67920 is composite. Its prime factorisation is
- 3
The divisors add up to 211296; without 67920 itself that is 143376, so 67920 is abundant (143376 is more than 67920). Euler's totient φ(67920) = 18048 numbers up to 67920 share no factor with it.
- 4
The digits of 67920 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 130 steps to reach 1.
LaTeX source of the formulas on this page
\[ 67920 = 2^{4} \times 3 \times 5 \times 283 \]67920 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 211296 |
| Euler totient φ(n) | 18048 |
| Square | 4613126400 |
| Cube | 313323545088000 |
| Square root | 260.614658 (= 4√4245) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 130 |
| Scientific notation | 6.792 × |
67920 in other forms
| Form | Value |
|---|---|
| In words | sixty-seven thousand nine hundred and twenty |
| Binary (base 2) | 10000100101010000 |
| Octal (base 8) | 204520 |
| Hexadecimal (base 16) | 10950 |
| Base 3 | 10110011120 |
| As time | 67920 seconds = 18 h 52 min 0 s |
Is 67920 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (67920 ÷ 2 = 33960) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (67920 ÷ 3 = 22640) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (67920 ÷ 4 = 16980) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (67920 ÷ 5 = 13584) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (67920 ÷ 6 = 11320) | 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 (67920 ÷ 8 = 8490) | 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 (67920 ÷ 10 = 6792) | 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 (67920 ÷ 12 = 5660) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 67920 a prime number?
No. 67920 = × 3 × 5 × 283, so it is divisible by 2.
What are the factors of 67920?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, 283, 566, 849, 1132, 1415, 1698, 2264, 2830, 3396, 4245, 4528, 5660, 6792, 8490, 11320, 13584, 16980, 22640, 33960, 67920.
What is 67920 in binary?
10000100101010000 (hexadecimal 10950, octal 204520).
What is the square root of 67920?
About 260.6147, exactly 4√4245.
Is 67920 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 67920?
67920 is a Harshad number: divisible by its digit sum 24.