The number 77540
77540 is a composite number with 12 divisors. Its prime factorisation is × 5 × 3877. Divisors (12): 1, 2, 4, 5, 10, 20, 3877, 7754, 15508, 19385, 38770, 77540.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 77540: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
77540 is composite. Its prime factorisation is
- 3
The divisors add up to 162876; without 77540 itself that is 85336, so 77540 is abundant (85336 is more than 77540). Euler's totient φ(77540) = 31008 numbers up to 77540 share no factor with it.
- 4
The digits of 77540 add up to 23, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 76 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77540 = 2^{2} \times 5 \times 3877 \]77540 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 162876 |
| Euler totient φ(n) | 31008 |
| Square | 6012451600 |
| Cube | 466205497064000 |
| Square root | 278.460051 (= 2√19385) |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 76 |
| Scientific notation | 7.754 × |
77540 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand five hundred and forty |
| Binary (base 2) | 10010111011100100 |
| Octal (base 8) | 227344 |
| Hexadecimal (base 16) | 12EE4 |
| Base 3 | 10221100212 |
| As time | 77540 seconds = 21 h 32 min 20 s |
Is 77540 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77540 ÷ 2 = 38770) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77540 ÷ 4 = 19385) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (77540 ÷ 5 = 15508) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | 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 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (77540 ÷ 10 = 7754) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77540 a prime number?
No. 77540 = × 5 × 3877, so it is divisible by 2.
What are the factors of 77540?
1, 2, 4, 5, 10, 20, 3877, 7754, 15508, 19385, 38770, 77540.
What is 77540 in binary?
10010111011100100 (hexadecimal 12EE4, octal 227344).
What is the square root of 77540?
About 278.4601, exactly 2√19385.
Is 77540 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 77540?
77540 is a happy number: repeatedly adding the squares of its digits reaches 1.