The number 77504
77504 is a composite number with 28 divisors. Its prime factorisation is × 7 × 173. Divisors (28): 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 173, 224, 346, 448 … 77504.
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How to work it out
- 1
What is special about 77504: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
77504 is composite. Its prime factorisation is
- 3
The divisors add up to 176784; without 77504 itself that is 99280, so 77504 is abundant (99280 is more than 77504). Euler's totient φ(77504) = 33024 numbers up to 77504 share no factor with it.
- 4
The digits of 77504 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
\[ 77504 = 2^{6} \times 7 \times 173 \]77504 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 28 |
| Sum of divisors | 176784 |
| Euler totient φ(n) | 33024 |
| Square | 6006870016 |
| Cube | 465556453720064 |
| Square root | 278.395402 (= 8√1211) |
| Digit sum / digital root | 23 / 5 |
| Collatz steps to 1 | 76 |
| Scientific notation | 7.7504 × |
77504 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand five hundred and four |
| Binary (base 2) | 10010111011000000 |
| Octal (base 8) | 227300 |
| Hexadecimal (base 16) | 12EC0 |
| Base 3 | 10221022112 |
| As time | 77504 seconds = 21 h 31 min 44 s |
Is 77504 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77504 ÷ 2 = 38752) | 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 (77504 ÷ 4 = 19376) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (77504 ÷ 7 = 11072) | 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 (77504 ÷ 8 = 9688) | 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 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | 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 77504 a prime number?
No. 77504 = × 7 × 173, so it is divisible by 2.
What are the factors of 77504?
1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 173, 224, 346, 448, 692, 1211, 1384, 2422, 2768, 4844, 5536, 9688, 11072, 19376, 38752, 77504.
What is 77504 in binary?
10010111011000000 (hexadecimal 12EC0, octal 227300).
What is the square root of 77504?
About 278.3954, exactly 8√1211.
Is 77504 divisible by 3?
No. Its digits add up to 23, which is not a multiple of 3.
What is special about the number 77504?
77504 is a happy number: repeatedly adding the squares of its digits reaches 1.