The number 777
777 is a palindrome: it reads 777 backwards too. Its prime factorisation is 3 × 7 × 37. Divisors (8): 1, 3, 7, 21, 37, 111, 259, 777.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 777: a palindrome: it reads 777 backwards too; a Harshad number: divisible by its digit sum 21.
- 2
777 is composite. Its prime factorisation is
- 3
The divisors add up to 1216; without 777 itself that is 439, so 777 is deficient (439 is less than 777). Euler's totient φ(777) = 432 numbers up to 777 share no factor with it.
- 4
The digits of 777 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 33 steps to reach 1.
LaTeX source of the formulas on this page
\[ 777 = 3 \times 7 \times 37 \]
777 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 8 |
| Sum of divisors | 1216 |
| Euler totient φ(n) | 432 |
| Square | 603729 |
| Cube | 469097433 |
| Square root | 27.874720 |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 33 |
| Scientific notation | 7.77 × |
777 in other forms
| Form | Value |
|---|---|
| In words | seven hundred and seventy-seven |
| Roman numerals | DCCLXXVII |
| Binary (base 2) | 1100001001 |
| Octal (base 8) | 1411 |
| Hexadecimal (base 16) | 309 |
| Base 3 | 1001210 |
| As time | 777 seconds = 12 min 57 s |
Is 777 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (777 ÷ 3 = 259) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 3) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (777 ÷ 7 = 111) | 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 1) | 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 7) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 9) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 777 a prime number?
No. 777 = 3 × 7 × 37, so it is divisible by 3.
What are the factors of 777?
1, 3, 7, 21, 37, 111, 259, 777.
What is 777 in binary?
1100001001 (hexadecimal 309, octal 1411).
What is the square root of 777?
About 27.8747.
What is 777 in Roman numerals?
DCCLXXVII.
Is 777 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 777?
777 is a palindrome: it reads 777 backwards too; a Harshad number: divisible by its digit sum 21.