The number 75684
75684 is a composite number with 48 divisors. Its prime factorisation is × 3 × 7 × 17 × 53. Divisors (48): 1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 53, 68 … 75684.
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How to work it out
- 1
What is special about 75684: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
75684 is composite. Its prime factorisation is
- 3
The divisors add up to 217728; without 75684 itself that is 142044, so 75684 is abundant (142044 is more than 75684). Euler's totient φ(75684) = 19968 numbers up to 75684 share no factor with it.
- 4
The digits of 75684 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 75684 = 2^{2} \times 3 \times 7 \times 17 \times 53 \]75684 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 217728 |
| Euler totient φ(n) | 19968 |
| Square | 5728067856 |
| Cube | 433523087613504 |
| Square root | 275.107252 (= 2√18921) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 107 |
| Scientific notation | 7.5684 × |
75684 in other forms
| Form | Value |
|---|---|
| In words | seventy-five thousand six hundred and eighty-four |
| Binary (base 2) | 10010011110100100 |
| Octal (base 8) | 223644 |
| Hexadecimal (base 16) | 127A4 |
| Base 3 | 10211211010 |
| As time | 75684 seconds = 21 h 1 min 24 s |
Is 75684 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (75684 ÷ 2 = 37842) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (75684 ÷ 3 = 25228) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (75684 ÷ 4 = 18921) | 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 (75684 ÷ 6 = 12614) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (75684 ÷ 7 = 10812) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | 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 | Yes (75684 ÷ 12 = 6307) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 75684 a prime number?
No. 75684 = × 3 × 7 × 17 × 53, so it is divisible by 2.
What are the factors of 75684?
1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 53, 68, 84, 102, 106, 119, 159, 204, 212, 238, 318, 357, 371, 476, 636, 714, 742, 901, 1113, 1428, 1484, 1802, 2226, 2703, 3604, 4452, 5406, 6307, 10812, 12614, 18921, 25228, 37842, 75684.
What is 75684 in binary?
10010011110100100 (hexadecimal 127A4, octal 223644).
What is the square root of 75684?
About 275.1073, exactly 2√18921.
Is 75684 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 75684?
75684 is a happy number: repeatedly adding the squares of its digits reaches 1.