The number 71664
71664 is a composite number with 20 divisors. Its prime factorisation is × 3 × 1493. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1493, 2986, 4479, 5972, 8958, 11944 … 71664.
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How to work it out
- 1
What is special about 71664: a Harshad number: divisible by its digit sum 24.
- 2
71664 is composite. Its prime factorisation is
- 3
The divisors add up to 185256; without 71664 itself that is 113592, so 71664 is abundant (113592 is more than 71664). Euler's totient φ(71664) = 23872 numbers up to 71664 share no factor with it.
- 4
The digits of 71664 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 143 steps to reach 1.
LaTeX source of the formulas on this page
\[ 71664 = 2^{4} \times 3 \times 1493 \]71664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 185256 |
| Euler totient φ(n) | 23872 |
| Square | 5135728896 |
| Cube | 368046875602944 |
| Square root | 267.701326 (= 4√4479) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 143 |
| Scientific notation | 7.1664 × |
71664 in other forms
| Form | Value |
|---|---|
| In words | seventy-one thousand six hundred and sixty-four |
| Binary (base 2) | 10001011111110000 |
| Octal (base 8) | 213760 |
| Hexadecimal (base 16) | 117F0 |
| Base 3 | 10122022020 |
| As time | 71664 seconds = 19 h 54 min 24 s |
Is 71664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (71664 ÷ 2 = 35832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (71664 ÷ 3 = 23888) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (71664 ÷ 4 = 17916) | 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 (71664 ÷ 6 = 11944) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | 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 (71664 ÷ 8 = 8958) | 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 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (71664 ÷ 12 = 5972) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 71664 a prime number?
No. 71664 = × 3 × 1493, so it is divisible by 2.
What are the factors of 71664?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1493, 2986, 4479, 5972, 8958, 11944, 17916, 23888, 35832, 71664.
What is 71664 in binary?
10001011111110000 (hexadecimal 117F0, octal 213760).
What is the square root of 71664?
About 267.7013, exactly 4√4479.
Is 71664 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 71664?
71664 is a Harshad number: divisible by its digit sum 24.