The number 77724
77724 is a composite number with 36 divisors. Its prime factorisation is × × 17 × 127. Divisors (36): 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 127, 153 … 77724.
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How to work it out
- 1
What is special about 77724: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
77724 is composite. Its prime factorisation is
- 3
The divisors add up to 209664; without 77724 itself that is 131940, so 77724 is abundant (131940 is more than 77724). Euler's totient φ(77724) = 24192 numbers up to 77724 share no factor with it.
- 4
The digits of 77724 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 125 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77724 = 2^{2} \times 3^{2} \times 17 \times 127 \]77724 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 209664 |
| Euler totient φ(n) | 24192 |
| Square | 6041020176 |
| Cube | 469532252159424 |
| Square root | 278.790244 (= 6√2159) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 125 |
| Scientific notation | 7.7724 × |
77724 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand seven hundred and twenty-four |
| Binary (base 2) | 10010111110011100 |
| Octal (base 8) | 227634 |
| Hexadecimal (base 16) | 12F9C |
| Base 3 | 10221121200 |
| As time | 77724 seconds = 21 h 35 min 24 s |
Is 77724 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77724 ÷ 2 = 38862) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77724 ÷ 3 = 25908) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77724 ÷ 4 = 19431) | 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 | Yes (77724 ÷ 6 = 12954) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (77724 ÷ 9 = 8636) | 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 | Yes (77724 ÷ 12 = 6477) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77724 a prime number?
No. 77724 = × × 17 × 127, so it is divisible by 2.
What are the factors of 77724?
1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 127, 153, 204, 254, 306, 381, 508, 612, 762, 1143, 1524, 2159, 2286, 4318, 4572, 6477, 8636, 12954, 19431, 25908, 38862, 77724.
What is 77724 in binary?
10010111110011100 (hexadecimal 12F9C, octal 227634).
What is the square root of 77724?
About 278.7902, exactly 6√2159.
Is 77724 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 77724?
77724 is a happy number: repeatedly adding the squares of its digits reaches 1.