The number 77424
77424 is a composite number with 20 divisors. Its prime factorisation is × 3 × 1613. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1613, 3226, 4839, 6452, 9678, 12904 … 77424.
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How to work it out
- 1
What is special about 77424: a Harshad number: divisible by its digit sum 24.
- 2
77424 is composite. Its prime factorisation is
- 3
The divisors add up to 200136; without 77424 itself that is 122712, so 77424 is abundant (122712 is more than 77424). Euler's totient φ(77424) = 25792 numbers up to 77424 share no factor with it.
- 4
The digits of 77424 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 169 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77424 = 2^{4} \times 3 \times 1613 \]77424 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 200136 |
| Euler totient φ(n) | 25792 |
| Square | 5994475776 |
| Cube | 464116292481024 |
| Square root | 278.251685 (= 4√4839) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 169 |
| Scientific notation | 7.7424 × |
77424 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand four hundred and twenty-four |
| Binary (base 2) | 10010111001110000 |
| Octal (base 8) | 227160 |
| Hexadecimal (base 16) | 12E70 |
| Base 3 | 10221012120 |
| As time | 77424 seconds = 21 h 30 min 24 s |
Is 77424 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77424 ÷ 2 = 38712) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77424 ÷ 3 = 25808) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77424 ÷ 4 = 19356) | 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 (77424 ÷ 6 = 12904) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (77424 ÷ 8 = 9678) | 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 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77424 ÷ 12 = 6452) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77424 a prime number?
No. 77424 = × 3 × 1613, so it is divisible by 2.
What are the factors of 77424?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1613, 3226, 4839, 6452, 9678, 12904, 19356, 25808, 38712, 77424.
What is 77424 in binary?
10010111001110000 (hexadecimal 12E70, octal 227160).
What is the square root of 77424?
About 278.2517, exactly 4√4839.
Is 77424 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 77424?
77424 is a Harshad number: divisible by its digit sum 24.