The number 35664
35664 is a composite number with 20 divisors. Its prime factorisation is × 3 × 743. Divisors (20): 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 743, 1486, 2229, 2972, 4458, 5944 … 35664.
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How to work it out
- 1
What is special about 35664: a Harshad number: divisible by its digit sum 24.
- 2
35664 is composite. Its prime factorisation is
- 3
The divisors add up to 92256; without 35664 itself that is 56592, so 35664 is abundant (56592 is more than 35664). Euler's totient φ(35664) = 11872 numbers up to 35664 share no factor with it.
- 4
The digits of 35664 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 49 steps to reach 1.
LaTeX source of the formulas on this page
\[ 35664 = 2^{4} \times 3 \times 743 \]35664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 20 |
| Sum of divisors | 92256 |
| Euler totient φ(n) | 11872 |
| Square | 1271920896 |
| Cube | 45361786834944 |
| Square root | 188.849146 (= 4√2229) |
| Digit sum / digital root | 24 / 6 |
| Collatz steps to 1 | 49 |
| Scientific notation | 3.5664 × |
35664 in other forms
| Form | Value |
|---|---|
| In words | thirty-five thousand six hundred and sixty-four |
| Binary (base 2) | 1000101101010000 |
| Octal (base 8) | 105520 |
| Hexadecimal (base 16) | 8B50 |
| Base 3 | 1210220220 |
| As time | 35664 seconds = 9 h 54 min 24 s |
Is 35664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (35664 ÷ 2 = 17832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (35664 ÷ 3 = 11888) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (35664 ÷ 4 = 8916) | 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 (35664 ÷ 6 = 5944) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 (35664 ÷ 8 = 4458) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (35664 ÷ 12 = 2972) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 35664 a prime number?
No. 35664 = × 3 × 743, so it is divisible by 2.
What are the factors of 35664?
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 743, 1486, 2229, 2972, 4458, 5944, 8916, 11888, 17832, 35664.
What is 35664 in binary?
1000101101010000 (hexadecimal 8B50, octal 105520).
What is the square root of 35664?
About 188.8491, exactly 4√2229.
Is 35664 divisible by 3?
Yes. Its digits add up to 24, a multiple of 3.
What is special about the number 35664?
35664 is a Harshad number: divisible by its digit sum 24.