The number 48024
48024 is a composite number with 48 divisors. Its prime factorisation is × × 23 × 29. Divisors (48): 1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 29, 36, 46, 58, 69 … 48024.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 48024: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.
- 2
48024 is composite. Its prime factorisation is
- 3
The divisors add up to 140400; without 48024 itself that is 92376, so 48024 is abundant (92376 is more than 48024). Euler's totient φ(48024) = 14784 numbers up to 48024 share no factor with it.
- 4
The digits of 48024 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 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48024 = 2^{3} \times 3^{2} \times 23 \times 29 \]48024 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 140400 |
| Euler totient φ(n) | 14784 |
| Square | 2306304576 |
| Cube | 110757970957824 |
| Square root | 219.143788 (= 6√1334) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 44 |
| Scientific notation | 4.8024 × |
48024 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand and twenty-four |
| Binary (base 2) | 1011101110011000 |
| Octal (base 8) | 135630 |
| Hexadecimal (base 16) | BB98 |
| Base 3 | 2102212200 |
| As time | 48024 seconds = 13 h 20 min 24 s |
Is 48024 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48024 ÷ 2 = 24012) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48024 ÷ 3 = 16008) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48024 ÷ 4 = 12006) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (48024 ÷ 6 = 8004) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (48024 ÷ 8 = 6003) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (48024 ÷ 9 = 5336) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 9) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48024 ÷ 12 = 4002) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48024 a prime number?
No. 48024 = × × 23 × 29, so it is divisible by 2.
What are the factors of 48024?
1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 29, 36, 46, 58, 69, 72, 87, 92, 116, 138, 174, 184, 207, 232, 261, 276, 348, 414, 522, 552, 667, 696, 828, 1044, 1334, 1656, 2001, 2088, 2668, 4002, 5336, 6003, 8004, 12006, 16008, 24012, 48024.
What is 48024 in binary?
1011101110011000 (hexadecimal BB98, octal 135630).
What is the square root of 48024?
About 219.1438, exactly 6√1334.
Is 48024 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 48024?
48024 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 18.