The number 96480
96480 is a composite number with 72 divisors. Its prime factorisation is × × 5 × 67. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 96480.
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How to work it out
- 1
96480 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
96480 is composite. Its prime factorisation is
- 3
The divisors add up to 334152; without 96480 itself that is 237672, so 96480 is abundant (237672 is more than 96480). Euler's totient φ(96480) = 25344 numbers up to 96480 share no factor with it.
- 4
The digits of 96480 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 97 steps to reach 1.
LaTeX source of the formulas on this page
\[ 96480 = 2^{5} \times 3^{2} \times 5 \times 67 \]96480 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 334152 |
| Euler totient φ(n) | 25344 |
| Square | 9308390400 |
| Cube | 898073505792000 |
| Square root | 310.612299 (= 12√670) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 97 |
| Scientific notation | 9.648 × |
96480 in other forms
| Form | Value |
|---|---|
| In words | ninety-six thousand four hundred and eighty |
| Binary (base 2) | 10111100011100000 |
| Octal (base 8) | 274340 |
| Hexadecimal (base 16) | 178E0 |
| Base 3 | 11220100100 |
| As time | 96480 seconds = 26 h 48 min 0 s |
Is 96480 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (96480 ÷ 2 = 48240) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (96480 ÷ 3 = 32160) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (96480 ÷ 4 = 24120) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (96480 ÷ 5 = 19296) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (96480 ÷ 6 = 16080) | 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 (96480 ÷ 8 = 12060) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (96480 ÷ 9 = 10720) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (96480 ÷ 10 = 9648) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (96480 ÷ 12 = 8040) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 96480 a prime number?
No. 96480 = × × 5 × 67, so it is divisible by 2.
What are the factors of 96480?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 67, 72, 80, 90, 96, 120, 134, 144, 160, 180, 201, 240, 268, 288, 335, 360, 402, 480, 536, 603, 670, 720, 804, 1005, 1072, 1206, 1340, 1440, 1608, 2010, 2144, 2412, 2680, 3015, 3216, 4020, 4824, 5360, 6030, 6432, 8040, 9648, 10720, 12060, 16080, 19296, 24120, 32160, 48240, 96480.
What is 96480 in binary?
10111100011100000 (hexadecimal 178E0, octal 274340).
What is the square root of 96480?
About 310.6123, exactly 12√670.
Is 96480 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 96480?
It is a composite number with 72 divisors.