The number 43872
43872 is a composite number with 24 divisors. Its prime factorisation is × 3 × 457. Divisors (24): 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 457, 914, 1371, 1828 … 43872.
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How to work it out
- 1
What is special about 43872: a Harshad number: divisible by its digit sum 24.
- 2
43872 is composite. Its prime factorisation is
- 3
The divisors add up to 115416; without 43872 itself that is 71544, so 43872 is abundant (71544 is more than 43872). Euler's totient φ(43872) = 14592 numbers up to 43872 share no factor with it.
- 4
The digits of 43872 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 119 steps to reach 1.
LaTeX source of the formulas on this page
\[ 43872 = 2^{5} \times 3 \times 457 \]43872 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 115416 |
| Euler totient φ(n) | 14592 |
| Square | 1924752384 |
| Cube | 84442736590848 |
| Square root | 209.456439 (= 4√2742) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 119 |
| Scientific notation | 4.3872 × |
43872 in other forms
| Form | Value |
|---|---|
| In words | forty-three thousand eight hundred and seventy-two |
| Binary (base 2) | 1010101101100000 |
| Octal (base 8) | 125540 |
| Hexadecimal (base 16) | AB60 |
| Base 3 | 2020011220 |
| As time | 43872 seconds = 12 h 11 min 12 s |
Is 43872 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (43872 ÷ 2 = 21936) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (43872 ÷ 3 = 14624) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (43872 ÷ 4 = 10968) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (43872 ÷ 6 = 7312) | 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 (43872 ÷ 8 = 5484) | 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 | No (remainder 2) | 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 (43872 ÷ 12 = 3656) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 43872 a prime number?
No. 43872 = × 3 × 457, so it is divisible by 2.
What are the factors of 43872?
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 457, 914, 1371, 1828, 2742, 3656, 5484, 7312, 10968, 14624, 21936, 43872.
What is 43872 in binary?
1010101101100000 (hexadecimal AB60, octal 125540).
What is the square root of 43872?
About 209.4564, exactly 4√2742.
Is 43872 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 43872?
43872 is a Harshad number: divisible by its digit sum 24.