The number 43920
43920 is a composite number with 60 divisors. Its prime factorisation is × × 5 × 61. Divisors (60): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30 … 43920.
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How to work it out
- 1
What is special about 43920: a Harshad number: divisible by its digit sum 18.
- 2
43920 is composite. Its prime factorisation is
- 3
The divisors add up to 149916; without 43920 itself that is 105996, so 43920 is abundant (105996 is more than 43920). Euler's totient φ(43920) = 11520 numbers up to 43920 share no factor with it.
- 4
The digits of 43920 add up to 18, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 44 steps to reach 1.
LaTeX source of the formulas on this page
\[ 43920 = 2^{4} \times 3^{2} \times 5 \times 61 \]43920 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 60 |
| Sum of divisors | 149916 |
| Euler totient φ(n) | 11520 |
| Square | 1928966400 |
| Cube | 84720204288000 |
| Square root | 209.570990 (= 12√305) |
| Digit sum / digital root | 18 / 9 |
| Collatz steps to 1 | 44 |
| Scientific notation | 4.392 × |
43920 in other forms
| Form | Value |
|---|---|
| In words | forty-three thousand nine hundred and twenty |
| Binary (base 2) | 1010101110010000 |
| Octal (base 8) | 125620 |
| Hexadecimal (base 16) | AB90 |
| Base 3 | 2020020200 |
| As time | 43920 seconds = 12 h 12 min 0 s |
Is 43920 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (43920 ÷ 2 = 21960) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (43920 ÷ 3 = 14640) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (43920 ÷ 4 = 10980) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (43920 ÷ 5 = 8784) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (43920 ÷ 6 = 7320) | 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 (43920 ÷ 8 = 5490) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (43920 ÷ 9 = 4880) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (43920 ÷ 10 = 4392) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (43920 ÷ 12 = 3660) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 43920 a prime number?
No. 43920 = × × 5 × 61, so it is divisible by 2.
What are the factors of 43920?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 61, 72, 80, 90, 120, 122, 144, 180, 183, 240, 244, 305, 360, 366, 488, 549, 610, 720, 732, 915, 976, 1098, 1220, 1464, 1830, 2196, 2440, 2745, 2928, 3660, 4392, 4880, 5490, 7320, 8784, 10980, 14640, 21960, 43920.
What is 43920 in binary?
1010101110010000 (hexadecimal AB90, octal 125620).
What is the square root of 43920?
About 209.5710, exactly 12√305.
Is 43920 divisible by 3?
Yes. Its digits add up to 18, a multiple of 3.
What is special about the number 43920?
43920 is a Harshad number: divisible by its digit sum 18.