The number 48400
48400 is a perfect square (220²). Its prime factorisation is × × . Divisors (45): 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 40, 44, 50, 55, 80 … 48400.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 48400: a perfect square (220²); a Harshad number: divisible by its digit sum 16.
- 2
48400 is composite. Its prime factorisation is
- 3
The divisors add up to 127813; without 48400 itself that is 79413, so 48400 is abundant (79413 is more than 48400). Euler's totient φ(48400) = 17600 numbers up to 48400 share no factor with it.
- 4
The digits of 48400 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 70 steps to reach 1.
LaTeX source of the formulas on this page
\[ 48400 = 2^{4} \times 5^{2} \times 11^{2} \]48400 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 45 |
| Sum of divisors | 127813 |
| Euler totient φ(n) | 17600 |
| Square | 2342560000 |
| Cube | 113379904000000 |
| Square root | 220 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 70 |
| Scientific notation | 4.84 × |
| Perfect power |
48400 in other forms
| Form | Value |
|---|---|
| In words | forty-eight thousand four hundred |
| Binary (base 2) | 1011110100010000 |
| Octal (base 8) | 136420 |
| Hexadecimal (base 16) | BD10 |
| Base 3 | 2110101121 |
| As time | 48400 seconds = 13 h 26 min 40 s |
Is 48400 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (48400 ÷ 2 = 24200) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (48400 ÷ 4 = 12100) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (48400 ÷ 5 = 9680) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 2) | 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 (48400 ÷ 8 = 6050) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (48400 ÷ 10 = 4840) | A number is divisible by 10 if the last digit is 0. |
| 11 | Yes (48400 ÷ 11 = 4400) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 48400 a prime number?
No. 48400 = × × , so it is divisible by 2.
What are the factors of 48400?
1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 40, 44, 50, 55, 80, 88, 100, 110, 121, 176, 200, 220, 242, 275, 400, 440, 484, 550, 605, 880, 968, 1100, 1210, 1936, 2200, 2420, 3025, 4400, 4840, 6050, 9680, 12100, 24200, 48400.
What is 48400 in binary?
1011110100010000 (hexadecimal BD10, octal 136420).
What is the square root of 48400?
220, because 220 × 220 = 48400.
Is 48400 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 48400?
48400 is a perfect square (220²); a Harshad number: divisible by its digit sum 16.