The number 74688
74688 is a composite number with 28 divisors. Its prime factorisation is × 3 × 389. Divisors (28): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 389, 778 … 74688.
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How to work it out
- 1
74688 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
74688 is composite. Its prime factorisation is
- 3
The divisors add up to 198120; without 74688 itself that is 123432, so 74688 is abundant (123432 is more than 74688). Euler's totient φ(74688) = 24832 numbers up to 74688 share no factor with it.
- 4
The digits of 74688 add up to 33, 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
\[ 74688 = 2^{6} \times 3 \times 389 \]74688 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 198120 |
| Euler totient φ(n) | 24832 |
| Square | 5578297344 |
| Cube | 416631872028672 |
| Square root | 273.291054 (= 8√1167) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 37 |
| Scientific notation | 7.4688 × |
74688 in other forms
| Form | Value |
|---|---|
| In words | seventy-four thousand six hundred and eighty-eight |
| Binary (base 2) | 10010001111000000 |
| Octal (base 8) | 221700 |
| Hexadecimal (base 16) | 123C0 |
| Base 3 | 10210110020 |
| As time | 74688 seconds = 20 h 44 min 48 s |
Is 74688 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (74688 ÷ 2 = 37344) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (74688 ÷ 3 = 24896) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (74688 ÷ 4 = 18672) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (74688 ÷ 6 = 12448) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (74688 ÷ 8 = 9336) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (74688 ÷ 12 = 6224) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 74688 a prime number?
No. 74688 = × 3 × 389, so it is divisible by 2.
What are the factors of 74688?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 389, 778, 1167, 1556, 2334, 3112, 4668, 6224, 9336, 12448, 18672, 24896, 37344, 74688.
What is 74688 in binary?
10010001111000000 (hexadecimal 123C0, octal 221700).
What is the square root of 74688?
About 273.2911, exactly 8√1167.
Is 74688 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 74688?
It is a composite number with 28 divisors.