The number 77976
77976 is a composite number with 48 divisors. Its prime factorisation is × × . Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 27, 36, 38, 54, 57 … 77976.
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How to work it out
- 1
What is special about 77976: a Harshad number: divisible by its digit sum 36.
- 2
77976 is composite. Its prime factorisation is
- 3
The divisors add up to 228600; without 77976 itself that is 150624, so 77976 is abundant (150624 is more than 77976). Euler's totient φ(77976) = 24624 numbers up to 77976 share no factor with it.
- 4
The digits of 77976 add up to 36, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77976 = 2^{3} \times 3^{3} \times 19^{2} \]77976 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 228600 |
| Euler totient φ(n) | 24624 |
| Square | 6080256576 |
| Cube | 474114086770176 |
| Square root | 279.241831 (= 114√6) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.7976 × |
77976 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand nine hundred and seventy-six |
| Binary (base 2) | 10011000010011000 |
| Octal (base 8) | 230230 |
| Hexadecimal (base 16) | 13098 |
| Base 3 | 10221222000 |
| As time | 77976 seconds = 21 h 39 min 36 s |
Is 77976 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77976 ÷ 2 = 38988) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77976 ÷ 3 = 25992) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77976 ÷ 4 = 19494) | 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 (77976 ÷ 6 = 12996) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (77976 ÷ 8 = 9747) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (77976 ÷ 9 = 8664) | 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 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77976 ÷ 12 = 6498) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77976 a prime number?
No. 77976 = × × , so it is divisible by 2.
What are the factors of 77976?
1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 27, 36, 38, 54, 57, 72, 76, 108, 114, 152, 171, 216, 228, 342, 361, 456, 513, 684, 722, 1026, 1083, 1368, 1444, 2052, 2166, 2888, 3249, 4104, 4332, 6498, 8664, 9747, 12996, 19494, 25992, 38988, 77976.
What is 77976 in binary?
10011000010011000 (hexadecimal 13098, octal 230230).
What is the square root of 77976?
About 279.2418, exactly 114√6.
Is 77976 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 77976?
77976 is a Harshad number: divisible by its digit sum 36.