The number 41664
41664 is a composite number with 56 divisors. Its prime factorisation is × 3 × 7 × 31. Divisors (56): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 31, 32, 42 … 41664.
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How to work it out
- 1
What is special about 41664: a Harshad number: divisible by its digit sum 21.
- 2
41664 is composite. Its prime factorisation is
- 3
The divisors add up to 130048; without 41664 itself that is 88384, so 41664 is abundant (88384 is more than 41664). Euler's totient φ(41664) = 11520 numbers up to 41664 share no factor with it.
- 4
The digits of 41664 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 106 steps to reach 1.
LaTeX source of the formulas on this page
\[ 41664 = 2^{6} \times 3 \times 7 \times 31 \]41664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 56 |
| Sum of divisors | 130048 |
| Euler totient φ(n) | 11520 |
| Square | 1735888896 |
| Cube | 72324074962944 |
| Square root | 204.117613 (= 8√651) |
| Digit sum / digital root | 21 / 3 |
| Collatz steps to 1 | 106 |
| Scientific notation | 4.1664 × |
41664 in other forms
| Form | Value |
|---|---|
| In words | forty-one thousand six hundred and sixty-four |
| Binary (base 2) | 1010001011000000 |
| Octal (base 8) | 121300 |
| Hexadecimal (base 16) | A2C0 |
| Base 3 | 2010011010 |
| As time | 41664 seconds = 11 h 34 min 24 s |
Is 41664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (41664 ÷ 2 = 20832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (41664 ÷ 3 = 13888) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (41664 ÷ 4 = 10416) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (41664 ÷ 6 = 6944) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (41664 ÷ 7 = 5952) | 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 (41664 ÷ 8 = 5208) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (41664 ÷ 12 = 3472) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 41664 a prime number?
No. 41664 = × 3 × 7 × 31, so it is divisible by 2.
What are the factors of 41664?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 31, 32, 42, 48, 56, 62, 64, 84, 93, 96, 112, 124, 168, 186, 192, 217, 224, 248, 336, 372, 434, 448, 496, 651, 672, 744, 868, 992, 1302, 1344, 1488, 1736, 1984, 2604, 2976, 3472, 5208, 5952, 6944, 10416, 13888, 20832, 41664.
What is 41664 in binary?
1010001011000000 (hexadecimal A2C0, octal 121300).
What is the square root of 41664?
About 204.1176, exactly 8√651.
Is 41664 divisible by 3?
Yes. Its digits add up to 21, a multiple of 3.
What is special about the number 41664?
41664 is a Harshad number: divisible by its digit sum 21.