The number 77977
77977 is a palindromic prime: it reads the same backwards and is prime, the 7660th prime number and a palindrome: it reads 77977 backwards too. Its only divisors are 1 and 77977.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77977: a palindromic prime: it reads the same backwards and is prime; the 7660th prime number; a palindrome: it reads 77977 backwards too.
- 2
77977 is prime, so its only factors are 1 and 77977. It is the 7660th prime; the next prime is 77983 and the one before is 77969.
- 3
The divisors add up to 77978; without 77977 itself that is 1, so 77977 is deficient (1 is less than 77977). Euler's totient φ(77977) = 77976 numbers up to 77977 share no factor with it.
- 4
The digits of 77977 add up to 37, and repeating that until one digit is left gives the digital root 1. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
77977 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 77978 |
| Euler totient φ(n) | 77976 |
| Square | 6080412529 |
| Cube | 474132327773833 |
| Square root | 279.243621 |
| Digit sum / digital root | 37 / 1 |
| Collatz steps to 1 | 107 |
| Scientific notation | 7.7977 × |
77977 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand nine hundred and seventy-seven |
| Binary (base 2) | 10011000010011001 |
| Octal (base 8) | 230231 |
| Hexadecimal (base 16) | 13099 |
| Base 3 | 10221222001 |
| As time | 77977 seconds = 21 h 39 min 37 s |
Is 77977 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 | No (remainder 1) | 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 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 1) | 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 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77977 a prime number?
Yes. 77977 is divisible only by 1 and itself.
What are the factors of 77977?
1, 77977.
What is 77977 in binary?
10011000010011001 (hexadecimal 13099, octal 230231).
What is the square root of 77977?
About 279.2436.
Is 77977 divisible by 3?
No. Its digits add up to 37, which is not a multiple of 3.
What is special about the number 77977?
77977 is a palindromic prime: it reads the same backwards and is prime; the 7660th prime number; a palindrome: it reads 77977 backwards too.