The number 61776
61776 is a triangular number: 1 + 2 + … + 351 = 61776. Its prime factorisation is × × 11 × 13. Divisors (80): 1, 2, 3, 4, 6, 8, 9, 11, 12, 13, 16, 18, 22, 24, 26, 27 … 61776.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 61776: a triangular number: 1 + 2 + … + 351 = 61776; a Harshad number: divisible by its digit sum 27.
- 2
61776 is composite. Its prime factorisation is
- 3
The divisors add up to 208320; without 61776 itself that is 146544, so 61776 is abundant (146544 is more than 61776). Euler's totient φ(61776) = 17280 numbers up to 61776 share no factor with it.
- 4
The digits of 61776 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 29 steps to reach 1.
LaTeX source of the formulas on this page
\[ 61776 = 2^{4} \times 3^{3} \times 11 \times 13 \]61776 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 208320 |
| Euler totient φ(n) | 17280 |
| Square | 3816274176 |
| Cube | 235754153496576 |
| Square root | 248.547782 (= 12√429) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 29 |
| Scientific notation | 6.1776 × |
61776 in other forms
| Form | Value |
|---|---|
| In words | sixty-one thousand seven hundred and seventy-six |
| Binary (base 2) | 1111000101010000 |
| Octal (base 8) | 170520 |
| Hexadecimal (base 16) | F150 |
| Base 3 | 10010202000 |
| As time | 61776 seconds = 17 h 9 min 36 s |
Is 61776 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (61776 ÷ 2 = 30888) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (61776 ÷ 3 = 20592) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (61776 ÷ 4 = 15444) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (61776 ÷ 6 = 10296) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (61776 ÷ 8 = 7722) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (61776 ÷ 9 = 6864) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (61776 ÷ 11 = 5616) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (61776 ÷ 12 = 5148) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 61776 a prime number?
No. 61776 = × × 11 × 13, so it is divisible by 2.
What are the factors of 61776?
1, 2, 3, 4, 6, 8, 9, 11, 12, 13, 16, 18, 22, 24, 26, 27, 33, 36, 39, 44, 48, 52, 54, 66, 72, 78, 88, 99, 104, 108, 117, 132, 143, 144, 156, 176, 198, 208, 216, 234, 264, 286, 297, 312, 351, 396, 429, 432, 468, 528, 572, 594, 624, 702, 792, 858, 936, 1144, 1188, 1287, 1404, 1584, 1716, 1872, 2288, 2376, 2574, 2808, 3432, 3861, 4752, 5148, 5616, 6864, 7722, 10296, 15444, 20592, 30888, 61776.
What is 61776 in binary?
1111000101010000 (hexadecimal F150, octal 170520).
What is the square root of 61776?
About 248.5478, exactly 12√429.
Is 61776 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 61776?
61776 is a triangular number: 1 + 2 + … + 351 = 61776; a Harshad number: divisible by its digit sum 27.