The number 77988
77988 is a composite number with 24 divisors. Its prime factorisation is × 3 × 67 × 97. Divisors (24): 1, 2, 3, 4, 6, 12, 67, 97, 134, 194, 201, 268, 291, 388, 402, 582 … 77988.
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How to work it out
- 1
77988 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77988 is composite. Its prime factorisation is
- 3
The divisors add up to 186592; without 77988 itself that is 108604, so 77988 is abundant (108604 is more than 77988). Euler's totient φ(77988) = 25344 numbers up to 77988 share no factor with it.
- 4
The digits of 77988 add up to 39, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 169 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77988 = 2^{2} \times 3 \times 67 \times 97 \]77988 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 186592 |
| Euler totient φ(n) | 25344 |
| Square | 6082128144 |
| Cube | 474333009694272 |
| Square root | 279.263317 (= 2√19497) |
| Digit sum / digital root | 39 / 3 |
| Collatz steps to 1 | 169 |
| Scientific notation | 7.7988 × |
77988 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand nine hundred and eighty-eight |
| Binary (base 2) | 10011000010100100 |
| Octal (base 8) | 230244 |
| Hexadecimal (base 16) | 130A4 |
| Base 3 | 10221222110 |
| As time | 77988 seconds = 21 h 39 min 48 s |
Is 77988 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77988 ÷ 2 = 38994) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77988 ÷ 3 = 25996) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77988 ÷ 4 = 19497) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77988 ÷ 6 = 12998) | 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 | 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 8) | 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 | Yes (77988 ÷ 12 = 6499) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77988 a prime number?
No. 77988 = × 3 × 67 × 97, so it is divisible by 2.
What are the factors of 77988?
1, 2, 3, 4, 6, 12, 67, 97, 134, 194, 201, 268, 291, 388, 402, 582, 804, 1164, 6499, 12998, 19497, 25996, 38994, 77988.
What is 77988 in binary?
10011000010100100 (hexadecimal 130A4, octal 230244).
What is the square root of 77988?
About 279.2633, exactly 2√19497.
Is 77988 divisible by 3?
Yes. Its digits add up to 39, a multiple of 3.
What is special about the number 77988?
It is a composite number with 24 divisors.