The number 48800
48800 is a composite number with 36 divisors. Its prime factorisation is × × 61. Divisors (36): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 61, 80, 100, 122 … 48800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 48800: a Harshad number: divisible by its digit sum 20.
- 2
48800 is composite. Its prime factorisation is
- 3
The divisors add up to 121086; without 48800 itself that is 72286, so 48800 is abundant (72286 is more than 48800). Euler's totient φ(48800) = 19200 numbers up to 48800 share no factor with it.
- 4
The digits of 48800 add up to 20, and repeating that until one digit is left gives the digital root 2. The Collatz sequence (halve if even, else 3n+1) takes 114 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48800 = 2^{5} \times 5^{2} \times 61 \]48800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 121086 |
| Euler totient φ(n) | 19200 |
| Square | 2381440000 |
| Cube | 116214272000000 |
| Square root | 220.907220 (= 20√122) |
| Digit sum / digital root | 20 / 2 |
| Collatz steps to 1 | 114 |
| Scientific notation | 4.88 × |
48800 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand eight hundred |
| Binary (base 2) | 1011111010100000 |
| Octal (base 8) | 137240 |
| Hexadecimal (base 16) | BEA0 |
| Base 3 | 2110221102 |
| As time | 48800 seconds = 13 h 33 min 20 s |
Is 48800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48800 ÷ 2 = 24400) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48800 ÷ 4 = 12200) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (48800 ÷ 5 = 9760) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 3) | 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 (48800 ÷ 8 = 6100) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 2) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (48800 ÷ 10 = 4880) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 4) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48800 a prime number?
No. 48800 = × × 61, so it is divisible by 2.
What are the factors of 48800?
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 61, 80, 100, 122, 160, 200, 244, 305, 400, 488, 610, 800, 976, 1220, 1525, 1952, 2440, 3050, 4880, 6100, 9760, 12200, 24400, 48800.
What is 48800 in binary?
1011111010100000 (hexadecimal BEA0, octal 137240).
What is the square root of 48800?
About 220.9072, exactly 20√122.
Is 48800 divisible by 3?
No. Its digits add up to 20, which is not a multiple of 3.
What is special about the number 48800?
48800 is a Harshad number: divisible by its digit sum 20.