The number 67984
67984 is a composite number with 20 divisors. Its prime factorisation is × 7 × 607. Divisors (20): 1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 607, 1214, 2428, 4249, 4856, 8498 … 67984.
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How to work it out
- 1
67984 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
67984 is composite. Its prime factorisation is
- 3
The divisors add up to 150784; without 67984 itself that is 82800, so 67984 is abundant (82800 is more than 67984). Euler's totient φ(67984) = 29088 numbers up to 67984 share no factor with it.
- 4
The digits of 67984 add up to 34, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 130 steps to reach 1.
LaTeX source of the formulas on this page
\[ 67984 = 2^{4} \times 7 \times 607 \]67984 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 150784 |
| Euler totient φ(n) | 29088 |
| Square | 4621824256 |
| Cube | 314210100219904 |
| Square root | 260.737416 (= 4√4249) |
| Digit sum / digital root | 34 / 7 |
| Collatz steps to 1 | 130 |
| Scientific notation | 6.7984 × |
67984 in other forms
| Form | Value |
|---|---|
| In words | sixty-seven thousand nine hundred and eighty-four |
| Binary (base 2) | 10000100110010000 |
| Octal (base 8) | 204620 |
| Hexadecimal (base 16) | 10990 |
| Base 3 | 10110020221 |
| As time | 67984 seconds = 18 h 53 min 4 s |
Is 67984 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (67984 ÷ 2 = 33992) | 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 (67984 ÷ 4 = 16996) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | 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 (67984 ÷ 7 = 9712) | 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 (67984 ÷ 8 = 8498) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | 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 67984 a prime number?
No. 67984 = × 7 × 607, so it is divisible by 2.
What are the factors of 67984?
1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 607, 1214, 2428, 4249, 4856, 8498, 9712, 16996, 33992, 67984.
What is 67984 in binary?
10000100110010000 (hexadecimal 10990, octal 204620).
What is the square root of 67984?
About 260.7374, exactly 4√4249.
Is 67984 divisible by 3?
No. Its digits add up to 34, which is not a multiple of 3.
What is special about the number 67984?
It is a composite number with 20 divisors.