The number 77640
77640 is a composite number with 32 divisors. Its prime factorisation is × 3 × 5 × 647. Divisors (32): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 … 77640.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77640: a Harshad number: divisible by its digit sum 24.
- 2
77640 is composite. Its prime factorisation is
- 3
The divisors add up to 233280; without 77640 itself that is 155640, so 77640 is abundant (155640 is more than 77640). Euler's totient φ(77640) = 20672 numbers up to 77640 share no factor with it.
- 4
The digits of 77640 add up to 24, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 182 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77640 = 2^{3} \times 3 \times 5 \times 647 \]77640 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 233280 |
| Euler totient φ(n) | 20672 |
| Square | 6027969600 |
| Cube | 468011559744000 |
| Square root | 278.639552 (= 2√19410) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 182 |
| Scientific notation | 7.764 × |
77640 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand six hundred and forty |
| Binary (base 2) | 10010111101001000 |
| Octal (base 8) | 227510 |
| Hexadecimal (base 16) | 12F48 |
| Base 3 | 10221111120 |
| As time | 77640 seconds = 21 h 34 min 0 s |
Is 77640 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77640 ÷ 2 = 38820) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77640 ÷ 3 = 25880) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77640 ÷ 4 = 19410) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (77640 ÷ 5 = 15528) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77640 ÷ 6 = 12940) | 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 (77640 ÷ 8 = 9705) | 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 | Yes (77640 ÷ 10 = 7764) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77640 ÷ 12 = 6470) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77640 a prime number?
No. 77640 = × 3 × 5 × 647, so it is divisible by 2.
What are the factors of 77640?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, 647, 1294, 1941, 2588, 3235, 3882, 5176, 6470, 7764, 9705, 12940, 15528, 19410, 25880, 38820, 77640.
What is 77640 in binary?
10010111101001000 (hexadecimal 12F48, octal 227510).
What is the square root of 77640?
About 278.6396, exactly 2√19410.
Is 77640 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 77640?
77640 is a Harshad number: divisible by its digit sum 24.