The number 77940
77940 is a composite number with 36 divisors. Its prime factorisation is × × 5 × 433. Divisors (36): 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60 … 77940.
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How to work it out
- 1
77940 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
77940 is composite. Its prime factorisation is
- 3
The divisors add up to 236964; without 77940 itself that is 159024, so 77940 is abundant (159024 is more than 77940). Euler's totient φ(77940) = 20736 numbers up to 77940 share no factor with it.
- 4
The digits of 77940 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 50 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77940 = 2^{2} \times 3^{2} \times 5 \times 433 \]77940 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 236964 |
| Euler totient φ(n) | 20736 |
| Square | 6074643600 |
| Cube | 473457722184000 |
| Square root | 279.177363 (= 6√2165) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 50 |
| Scientific notation | 7.794 × |
77940 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand nine hundred and forty |
| Binary (base 2) | 10011000001110100 |
| Octal (base 8) | 230164 |
| Hexadecimal (base 16) | 13074 |
| Base 3 | 10221220200 |
| As time | 77940 seconds = 21 h 39 min 0 s |
Is 77940 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77940 ÷ 2 = 38970) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77940 ÷ 3 = 25980) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77940 ÷ 4 = 19485) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (77940 ÷ 5 = 15588) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77940 ÷ 6 = 12990) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 | Yes (77940 ÷ 9 = 8660) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (77940 ÷ 10 = 7794) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77940 ÷ 12 = 6495) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77940 a prime number?
No. 77940 = × × 5 × 433, so it is divisible by 2.
What are the factors of 77940?
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 433, 866, 1299, 1732, 2165, 2598, 3897, 4330, 5196, 6495, 7794, 8660, 12990, 15588, 19485, 25980, 38970, 77940.
What is 77940 in binary?
10011000001110100 (hexadecimal 13074, octal 230164).
What is the square root of 77940?
About 279.1774, exactly 6√2165.
Is 77940 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 77940?
It is a composite number with 36 divisors.