The number 48048
48048 is a composite number with 80 divisors. Its prime factorisation is × 3 × 7 × 11 × 13. Divisors (80): 1, 2, 3, 4, 6, 7, 8, 11, 12, 13, 14, 16, 21, 22, 24, 26 … 48048.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 48048: a Harshad number: divisible by its digit sum 24.
- 2
48048 is composite. Its prime factorisation is
- 3
The divisors add up to 166656; without 48048 itself that is 118608, so 48048 is abundant (118608 is more than 48048). Euler's totient φ(48048) = 11520 numbers up to 48048 share no factor with it.
- 4
The digits of 48048 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 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48048 = 2^{4} \times 3 \times 7 \times 11 \times 13 \]48048 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 166656 |
| Euler totient φ(n) | 11520 |
| Square | 2308610304 |
| Cube | 110924107886592 |
| Square root | 219.198540 (= 4√3003) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 44 |
| Scientific notation | 4.8048 × |
48048 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand and forty-eight |
| Binary (base 2) | 1011101110110000 |
| Octal (base 8) | 135660 |
| Hexadecimal (base 16) | BBB0 |
| Base 3 | 2102220120 |
| As time | 48048 seconds = 13 h 20 min 48 s |
Is 48048 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48048 ÷ 2 = 24024) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (48048 ÷ 3 = 16016) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48048 ÷ 4 = 12012) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (48048 ÷ 6 = 8008) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (48048 ÷ 7 = 6864) | 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 (48048 ÷ 8 = 6006) | 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 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (48048 ÷ 11 = 4368) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (48048 ÷ 12 = 4004) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48048 a prime number?
No. 48048 = × 3 × 7 × 11 × 13, so it is divisible by 2.
What are the factors of 48048?
1, 2, 3, 4, 6, 7, 8, 11, 12, 13, 14, 16, 21, 22, 24, 26, 28, 33, 39, 42, 44, 48, 52, 56, 66, 77, 78, 84, 88, 91, 104, 112, 132, 143, 154, 156, 168, 176, 182, 208, 231, 264, 273, 286, 308, 312, 336, 364, 429, 462, 528, 546, 572, 616, 624, 728, 858, 924, 1001, 1092, 1144, 1232, 1456, 1716, 1848, 2002, 2184, 2288, 3003, 3432, 3696, 4004, 4368, 6006, 6864, 8008, 12012, 16016, 24024, 48048.
What is 48048 in binary?
1011101110110000 (hexadecimal BBB0, octal 135660).
What is the square root of 48048?
About 219.1985, exactly 4√3003.
Is 48048 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 48048?
48048 is a Harshad number: divisible by its digit sum 24.