The number 77352
77352 is a composite number with 32 divisors. Its prime factorisation is × 3 × 11 × 293. Divisors (32): 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264 … 77352.
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How to work it out
- 1
What is special about 77352: a Harshad number: divisible by its digit sum 24.
- 2
77352 is composite. Its prime factorisation is
- 3
The divisors add up to 211680; without 77352 itself that is 134328, so 77352 is abundant (134328 is more than 77352). Euler's totient φ(77352) = 23360 numbers up to 77352 share no factor with it.
- 4
The digits of 77352 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 24 steps to reach 1.
LaTeX source of the formulas on this page
\[ 77352 = 2^{3} \times 3 \times 11 \times 293 \]77352 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 32 |
| Sum of divisors | 211680 |
| Euler totient φ(n) | 23360 |
| Square | 5983331904 |
| Cube | 462822689438208 |
| Square root | 278.122275 (= 2√19338) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 24 |
| Scientific notation | 7.7352 × |
77352 in other forms
| Form | Value |
|---|---|
| In words | seventy-seven thousand three hundred and fifty-two |
| Binary (base 2) | 10010111000101000 |
| Octal (base 8) | 227050 |
| Hexadecimal (base 16) | 12E28 |
| Base 3 | 10221002220 |
| As time | 77352 seconds = 21 h 29 min 12 s |
Is 77352 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (77352 ÷ 2 = 38676) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (77352 ÷ 3 = 25784) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (77352 ÷ 4 = 19338) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (77352 ÷ 6 = 12892) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (77352 ÷ 8 = 9669) | 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 2) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (77352 ÷ 11 = 7032) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (77352 ÷ 12 = 6446) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 77352 a prime number?
No. 77352 = × 3 × 11 × 293, so it is divisible by 2.
What are the factors of 77352?
1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264, 293, 586, 879, 1172, 1758, 2344, 3223, 3516, 6446, 7032, 9669, 12892, 19338, 25784, 38676, 77352.
What is 77352 in binary?
10010111000101000 (hexadecimal 12E28, octal 227050).
What is the square root of 77352?
About 278.1223, exactly 2√19338.
Is 77352 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 77352?
77352 is a Harshad number: divisible by its digit sum 24.