The number 49680
49680 is a composite number with 80 divisors. Its prime factorisation is × × 5 × 23. Divisors (80): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 23, 24 … 49680.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 49680: a Harshad number: divisible by its digit sum 27.
- 2
49680 is composite. Its prime factorisation is
- 3
The divisors add up to 178560; without 49680 itself that is 128880, so 49680 is abundant (128880 is more than 49680). Euler's totient φ(49680) = 12672 numbers up to 49680 share no factor with it.
- 4
The digits of 49680 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 158 steps to reach 1.
LaTeX source of the formulas on this page
\[ 49680 = 2^{4} \times 3^{3} \times 5 \times 23 \]49680 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 80 |
| Sum of divisors | 178560 |
| Euler totient φ(n) | 12672 |
| Square | 2468102400 |
| Cube | 122615327232000 |
| Square root | 222.890107 (= 12√345) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 158 |
| Scientific notation | 4.968 × |
49680 in other forms
| Form | Value |
|---|---|
| In words | forty-nine thousand six hundred and eighty |
| Binary (base 2) | 1100001000010000 |
| Octal (base 8) | 141020 |
| Hexadecimal (base 16) | C210 |
| Base 3 | 2112011000 |
| As time | 49680 seconds = 13 h 48 min 0 s |
Is 49680 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (49680 ÷ 2 = 24840) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (49680 ÷ 3 = 16560) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (49680 ÷ 4 = 12420) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (49680 ÷ 5 = 9936) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (49680 ÷ 6 = 8280) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (49680 ÷ 8 = 6210) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (49680 ÷ 9 = 5520) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (49680 ÷ 10 = 4968) | 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 | Yes (49680 ÷ 12 = 4140) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 49680 a prime number?
No. 49680 = × × 5 × 23, so it is divisible by 2.
What are the factors of 49680?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 23, 24, 27, 30, 36, 40, 45, 46, 48, 54, 60, 69, 72, 80, 90, 92, 108, 115, 120, 135, 138, 144, 180, 184, 207, 216, 230, 240, 270, 276, 345, 360, 368, 414, 432, 460, 540, 552, 621, 690, 720, 828, 920, 1035, 1080, 1104, 1242, 1380, 1656, 1840, 2070, 2160, 2484, 2760, 3105, 3312, 4140, 4968, 5520, 6210, 8280, 9936, 12420, 16560, 24840, 49680.
What is 49680 in binary?
1100001000010000 (hexadecimal C210, octal 141020).
What is the square root of 49680?
About 222.8901, exactly 12√345.
Is 49680 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 49680?
49680 is a Harshad number: divisible by its digit sum 27.