The number 61680
61680 is a composite number with 40 divisors. Its prime factorisation is × 3 × 5 × 257. Divisors (40): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48 … 61680.
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How to work it out
- 1
61680 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
61680 is composite. Its prime factorisation is
- 3
The divisors add up to 191952; without 61680 itself that is 130272, so 61680 is abundant (130272 is more than 61680). Euler's totient φ(61680) = 16384 numbers up to 61680 share no factor with it.
- 4
The digits of 61680 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 55 steps to reach 1.
LaTeX source of the formulas on this page
\[ 61680 = 2^{4} \times 3 \times 5 \times 257 \]61680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 191952 |
| Euler totient φ(n) | 16384 |
| Square | 3804422400 |
| Cube | 234656773632000 |
| Square root | 248.354585 (= 4√3855) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 55 |
| Scientific notation | 6.168 × |
61680 in other forms
| Form | Value |
|---|---|
| In words | sixty-one thousand six hundred and eighty |
| Binary (base 2) | 1111000011110000 |
| Octal (base 8) | 170360 |
| Hexadecimal (base 16) | F0F0 |
| Base 3 | 10010121110 |
| As time | 61680 seconds = 17 h 8 min 0 s |
Is 61680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (61680 ÷ 2 = 30840) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (61680 ÷ 3 = 20560) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (61680 ÷ 4 = 15420) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (61680 ÷ 5 = 12336) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (61680 ÷ 6 = 10280) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (61680 ÷ 8 = 7710) | 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 | Yes (61680 ÷ 10 = 6168) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (61680 ÷ 12 = 5140) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 61680 a prime number?
No. 61680 = × 3 × 5 × 257, so it is divisible by 2.
What are the factors of 61680?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, 257, 514, 771, 1028, 1285, 1542, 2056, 2570, 3084, 3855, 4112, 5140, 6168, 7710, 10280, 12336, 15420, 20560, 30840, 61680.
What is 61680 in binary?
1111000011110000 (hexadecimal F0F0, octal 170360).
What is the square root of 61680?
About 248.3546, exactly 4√3855.
Is 61680 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 61680?
It is a composite number with 40 divisors.