The number 49920
49920 is a composite number with 72 divisors. Its prime factorisation is × 3 × 5 × 13. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30 … 49920.
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How to work it out
- 1
What is special about 49920: a Harshad number: divisible by its digit sum 24.
- 2
49920 is composite. Its prime factorisation is
- 3
The divisors add up to 171696; without 49920 itself that is 121776, so 49920 is abundant (121776 is more than 49920). Euler's totient φ(49920) = 12288 numbers up to 49920 share no factor with it.
- 4
The digits of 49920 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 127 steps to reach 1.
LaTeX source of the formulas on this page
\[ 49920 = 2^{8} \times 3 \times 5 \times 13 \]49920 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 171696 |
| Euler totient φ(n) | 12288 |
| Square | 2492006400 |
| Cube | 124400959488000 |
| Square root | 223.427841 (= 16√195) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 127 |
| Scientific notation | 4.992 × |
49920 in other forms
| Form | Value |
|---|---|
| In words | forty-nine thousand nine hundred and twenty |
| Binary (base 2) | 1100001100000000 |
| Octal (base 8) | 141400 |
| Hexadecimal (base 16) | C300 |
| Base 3 | 2112110220 |
| As time | 49920 seconds = 13 h 52 min 0 s |
Is 49920 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (49920 ÷ 2 = 24960) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (49920 ÷ 3 = 16640) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (49920 ÷ 4 = 12480) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (49920 ÷ 5 = 9984) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (49920 ÷ 6 = 8320) | 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 (49920 ÷ 8 = 6240) | 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 | Yes (49920 ÷ 10 = 4992) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (49920 ÷ 12 = 4160) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 49920 a prime number?
No. 49920 = × 3 × 5 × 13, so it is divisible by 2.
What are the factors of 49920?
1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30, 32, 39, 40, 48, 52, 60, 64, 65, 78, 80, 96, 104, 120, 128, 130, 156, 160, 192, 195, 208, 240, 256, 260, 312, 320, 384, 390, 416, 480, 520, 624, 640, 768, 780, 832, 960, 1040, 1248, 1280, 1560, 1664, 1920, 2080, 2496, 3120, 3328, 3840, 4160, 4992, 6240, 8320, 9984, 12480, 16640, 24960, 49920.
What is 49920 in binary?
1100001100000000 (hexadecimal C300, octal 141400).
What is the square root of 49920?
About 223.4278, exactly 16√195.
Is 49920 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 49920?
49920 is a Harshad number: divisible by its digit sum 24.