The number 48480
48480 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 101. Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40 … 48480.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 48480: a Harshad number: divisible by its digit sum 24.
- 2
48480 is composite. Its prime factorisation is
- 3
The divisors add up to 154224; without 48480 itself that is 105744, so 48480 is abundant (105744 is more than 48480). Euler's totient φ(48480) = 12800 numbers up to 48480 share no factor with it.
- 4
The digits of 48480 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 145 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48480 = 2^{5} \times 3 \times 5 \times 101 \]48480 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 154224 |
| Euler totient φ(n) | 12800 |
| Square | 2350310400 |
| Cube | 113943048192000 |
| Square root | 220.181743 (= 4√3030) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 145 |
| Scientific notation | 4.848 × |
48480 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand four hundred and eighty |
| Binary (base 2) | 1011110101100000 |
| Octal (base 8) | 136540 |
| Hexadecimal (base 16) | BD60 |
| Base 3 | 2110111120 |
| As time | 48480 seconds = 13 h 28 min 0 s |
Is 48480 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48480 ÷ 2 = 24240) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48480 ÷ 3 = 16160) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48480 ÷ 4 = 12120) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (48480 ÷ 5 = 9696) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (48480 ÷ 6 = 8080) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (48480 ÷ 8 = 6060) | 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 | Yes (48480 ÷ 10 = 4848) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48480 ÷ 12 = 4040) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48480 a prime number?
No. 48480 = × 3 × 5 × 101, so it is divisible by 2.
What are the factors of 48480?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 101, 120, 160, 202, 240, 303, 404, 480, 505, 606, 808, 1010, 1212, 1515, 1616, 2020, 2424, 3030, 3232, 4040, 4848, 6060, 8080, 9696, 12120, 16160, 24240, 48480.
What is 48480 in binary?
1011110101100000 (hexadecimal BD60, octal 136540).
What is the square root of 48480?
About 220.1817, exactly 4√3030.
Is 48480 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 48480?
48480 is a Harshad number: divisible by its digit sum 24.