The number 37664
37664 is a composite number with 24 divisors. Its prime factorisation is × 11 × 107. Divisors (24): 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 107, 176, 214, 352, 428, 856 … 37664.
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How to work it out
- 1
37664 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
37664 is composite. Its prime factorisation is
- 3
The divisors add up to 81648; without 37664 itself that is 43984, so 37664 is abundant (43984 is more than 37664). Euler's totient φ(37664) = 16960 numbers up to 37664 share no factor with it.
- 4
The digits of 37664 add up to 26, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37664 = 2^{5} \times 11 \times 107 \]37664 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 24 |
| Sum of divisors | 81648 |
| Euler totient φ(n) | 16960 |
| Square | 1418576896 |
| Cube | 53429280210944 |
| Square root | 194.072152 (= 4√2354) |
| Digit sum / digital root | 26 / 8 |
| Collatz steps to 1 | 36 |
| Scientific notation | 3.7664 × |
37664 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand six hundred and sixty-four |
| Binary (base 2) | 1001001100100000 |
| Octal (base 8) | 111440 |
| Hexadecimal (base 16) | 9320 |
| Base 3 | 1220122222 |
| As time | 37664 seconds = 10 h 27 min 44 s |
Is 37664 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37664 ÷ 2 = 18832) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (37664 ÷ 4 = 9416) | 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 | No (remainder 2) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | 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 (37664 ÷ 8 = 4708) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 | Yes (37664 ÷ 11 = 3424) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37664 a prime number?
No. 37664 = × 11 × 107, so it is divisible by 2.
What are the factors of 37664?
1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 107, 176, 214, 352, 428, 856, 1177, 1712, 2354, 3424, 4708, 9416, 18832, 37664.
What is 37664 in binary?
1001001100100000 (hexadecimal 9320, octal 111440).
What is the square root of 37664?
About 194.0722, exactly 4√2354.
Is 37664 divisible by 3?
No. Its digits add up to 26, which is not a multiple of 3.
What is special about the number 37664?
It is a composite number with 24 divisors.