The number 76320
76320 is a composite number with 72 divisors. Its prime factorisation is × × 5 × 53. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 76320.
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How to work it out
- 1
What is special about 76320: a Harshad number: divisible by its digit sum 18.
- 2
76320 is composite. Its prime factorisation is
- 3
The divisors add up to 265356; without 76320 itself that is 189036, so 76320 is abundant (189036 is more than 76320). Euler's totient φ(76320) = 19968 numbers up to 76320 share no factor with it.
- 4
The digits of 76320 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 107 steps to reach 1.
LaTeX source of the formulas on this page
\[ 76320 = 2^{5} \times 3^{2} \times 5 \times 53 \]76320 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 265356 |
| Euler totient φ(n) | 19968 |
| Square | 5824742400 |
| Cube | 444544339968000 |
| Square root | 276.260746 (= 12√530) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 107 |
| Scientific notation | 7.632 × |
76320 in other forms
| Form | Value |
|---|---|
| In words | seventy-six thousand three hundred and twenty |
| Binary (base 2) | 10010101000100000 |
| Octal (base 8) | 225040 |
| Hexadecimal (base 16) | 12A20 |
| Base 3 | 10212200200 |
| As time | 76320 seconds = 21 h 12 min 0 s |
Is 76320 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (76320 ÷ 2 = 38160) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (76320 ÷ 3 = 25440) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (76320 ÷ 4 = 19080) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (76320 ÷ 5 = 15264) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (76320 ÷ 6 = 12720) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (76320 ÷ 8 = 9540) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (76320 ÷ 9 = 8480) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (76320 ÷ 10 = 7632) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (76320 ÷ 12 = 6360) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 76320 a prime number?
No. 76320 = × × 5 × 53, so it is divisible by 2.
What are the factors of 76320?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 53, 60, 72, 80, 90, 96, 106, 120, 144, 159, 160, 180, 212, 240, 265, 288, 318, 360, 424, 477, 480, 530, 636, 720, 795, 848, 954, 1060, 1272, 1440, 1590, 1696, 1908, 2120, 2385, 2544, 3180, 3816, 4240, 4770, 5088, 6360, 7632, 8480, 9540, 12720, 15264, 19080, 25440, 38160, 76320.
What is 76320 in binary?
10010101000100000 (hexadecimal 12A20, octal 225040).
What is the square root of 76320?
About 276.2607, exactly 12√530.
Is 76320 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 76320?
76320 is a Harshad number: divisible by its digit sum 18.