The number 35964
35964 is a composite number with 36 divisors. Its prime factorisation is × × 37. Divisors (36): 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 37, 54, 74, 81, 108, 111 … 35964.
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How to work it out
- 1
What is special about 35964: a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.
- 2
35964 is composite. Its prime factorisation is
- 3
The divisors add up to 96824; without 35964 itself that is 60860, so 35964 is abundant (60860 is more than 35964). Euler's totient φ(35964) = 11664 numbers up to 35964 share no factor with it.
- 4
The digits of 35964 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 142 steps to reach 1.
LaTeX source of the formulas on this page
\[ 35964 = 2^{2} \times 3^{5} \times 37 \]35964 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 36 |
| Sum of divisors | 96824 |
| Euler totient φ(n) | 11664 |
| Square | 1293409296 |
| Cube | 46516171921344 |
| Square root | 189.641768 (= 18√111) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 142 |
| Scientific notation | 3.5964 × |
35964 in other forms
| Form | Value |
|---|---|
| In words | thirty-five thousand nine hundred and sixty-four |
| Binary (base 2) | 1000110001111100 |
| Octal (base 8) | 106174 |
| Hexadecimal (base 16) | 8C7C |
| Base 3 | 1211100000 |
| As time | 35964 seconds = 9 h 59 min 24 s |
Is 35964 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (35964 ÷ 2 = 17982) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (35964 ÷ 3 = 11988) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (35964 ÷ 4 = 8991) | 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 (35964 ÷ 6 = 5994) | 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 | No (remainder 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (35964 ÷ 9 = 3996) | 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 5) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (35964 ÷ 12 = 2997) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 35964 a prime number?
No. 35964 = × × 37, so it is divisible by 2.
What are the factors of 35964?
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 37, 54, 74, 81, 108, 111, 148, 162, 222, 243, 324, 333, 444, 486, 666, 972, 999, 1332, 1998, 2997, 3996, 5994, 8991, 11988, 17982, 35964.
What is 35964 in binary?
1000110001111100 (hexadecimal 8C7C, octal 106174).
What is the square root of 35964?
About 189.6418, exactly 18√111.
Is 35964 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 35964?
35964 is a happy number: repeatedly adding the squares of its digits reaches 1; a Harshad number: divisible by its digit sum 27.