The number 67344
67344 is a composite number with 40 divisors. Its prime factorisation is × 3 × 23 × 61. Divisors (40): 1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 46, 48, 61, 69, 92, 122 … 67344.
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How to work it out
- 1
What is special about 67344: a Harshad number: divisible by its digit sum 24.
- 2
67344 is composite. Its prime factorisation is
- 3
The divisors add up to 184512; without 67344 itself that is 117168, so 67344 is abundant (117168 is more than 67344). Euler's totient φ(67344) = 21120 numbers up to 67344 share no factor with it.
- 4
The digits of 67344 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 37 steps to reach 1.
LaTeX source of the formulas on this page
\[ 67344 = 2^{4} \times 3 \times 23 \times 61 \]67344 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 184512 |
| Euler totient φ(n) | 21120 |
| Square | 4535214336 |
| Cube | 305419474243584 |
| Square root | 259.507225 (= 4√4209) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 37 |
| Scientific notation | 6.7344 × |
67344 in other forms
| Form | Value |
|---|---|
| In words | sixty-seven thousand three hundred and forty-four |
| Binary (base 2) | 10000011100010000 |
| Octal (base 8) | 203420 |
| Hexadecimal (base 16) | 10710 |
| Base 3 | 10102101020 |
| As time | 67344 seconds = 18 h 42 min 24 s |
Is 67344 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (67344 ÷ 2 = 33672) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (67344 ÷ 3 = 22448) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (67344 ÷ 4 = 16836) | 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 | Yes (67344 ÷ 6 = 11224) | 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 (67344 ÷ 8 = 8418) | 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 | No (remainder 4) | 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 (67344 ÷ 12 = 5612) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 67344 a prime number?
No. 67344 = × 3 × 23 × 61, so it is divisible by 2.
What are the factors of 67344?
1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 46, 48, 61, 69, 92, 122, 138, 183, 184, 244, 276, 366, 368, 488, 552, 732, 976, 1104, 1403, 1464, 2806, 2928, 4209, 5612, 8418, 11224, 16836, 22448, 33672, 67344.
What is 67344 in binary?
10000011100010000 (hexadecimal 10710, octal 203420).
What is the square root of 67344?
About 259.5072, exactly 4√4209.
Is 67344 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 67344?
67344 is a Harshad number: divisible by its digit sum 24.