The number 77964
77964 is a composite number with 24 divisors. Its prime factorisation is × 3 × 73 × 89. Divisors (24): 1, 2, 3, 4, 6, 12, 73, 89, 146, 178, 219, 267, 292, 356, 438, 534 … 77964.
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How to work it out
- 1
77964 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77964 is composite. Its prime factorisation is
- 3
The divisors add up to 186480; without 77964 itself that is 108516, so 77964 is abundant (108516 is more than 77964). Euler's totient φ(77964) = 25344 numbers up to 77964 share no factor with it.
- 4
The digits of 77964 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 138 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77964 = 2^{2} \times 3 \times 73 \times 89 \]77964 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 186480 |
| Euler totient φ(n) | 25344 |
| Square | 6078385296 |
| Cube | 473895231217344 |
| Square root | 279.220343 (= 2√19491) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 138 |
| Scientific notation | 7.7964 × |
77964 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand nine hundred and sixty-four |
| Binary (base 2) | 10011000010001100 |
| Octal (base 8) | 230214 |
| Hexadecimal (base 16) | 1308C |
| Base 3 | 10221221120 |
| As time | 77964 seconds = 21 h 39 min 24 s |
Is 77964 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77964 ÷ 2 = 38982) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77964 ÷ 3 = 25988) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77964 ÷ 4 = 19491) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77964 ÷ 6 = 12994) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 6) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | 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 | Yes (77964 ÷ 12 = 6497) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77964 a prime number?
No. 77964 = × 3 × 73 × 89, so it is divisible by 2.
What are the factors of 77964?
1, 2, 3, 4, 6, 12, 73, 89, 146, 178, 219, 267, 292, 356, 438, 534, 876, 1068, 6497, 12994, 19491, 25988, 38982, 77964.
What is 77964 in binary?
10011000010001100 (hexadecimal 1308C, octal 230214).
What is the square root of 77964?
About 279.2203, exactly 2√19491.
Is 77964 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 77964?
It is a composite number with 24 divisors.