The number 48180
48180 is a composite number with 48 divisors. Its prime factorisation is × 3 × 5 × 11 × 73. Divisors (48): 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55 … 48180.
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How to work it out
- 1
48180 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
48180 is composite. Its prime factorisation is
- 3
The divisors add up to 149184; without 48180 itself that is 101004, so 48180 is abundant (101004 is more than 48180). Euler's totient φ(48180) = 11520 numbers up to 48180 share no factor with it.
- 4
The digits of 48180 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48180 = 2^{2} \times 3 \times 5 \times 11 \times 73 \]48180 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 149184 |
| Euler totient φ(n) | 11520 |
| Square | 2321312400 |
| Cube | 111840831432000 |
| Square root | 219.499431 (= 2√12045) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 44 |
| Scientific notation | 4.818 × |
48180 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand one hundred and eighty |
| Binary (base 2) | 1011110000110100 |
| Octal (base 8) | 136064 |
| Hexadecimal (base 16) | BC34 |
| Base 3 | 2110002110 |
| As time | 48180 seconds = 13 h 23 min 0 s |
Is 48180 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48180 ÷ 2 = 24090) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48180 ÷ 3 = 16060) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48180 ÷ 4 = 12045) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (48180 ÷ 5 = 9636) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (48180 ÷ 6 = 8030) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (48180 ÷ 10 = 4818) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (48180 ÷ 11 = 4380) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48180 ÷ 12 = 4015) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48180 a prime number?
No. 48180 = × 3 × 5 × 11 × 73, so it is divisible by 2.
What are the factors of 48180?
1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 73, 110, 132, 146, 165, 219, 220, 292, 330, 365, 438, 660, 730, 803, 876, 1095, 1460, 1606, 2190, 2409, 3212, 4015, 4380, 4818, 8030, 9636, 12045, 16060, 24090, 48180.
What is 48180 in binary?
1011110000110100 (hexadecimal BC34, octal 136064).
What is the square root of 48180?
About 219.4994, exactly 2√12045.
Is 48180 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 48180?
It is a composite number with 48 divisors.