The number 37688
37688 is a composite number with 16 divisors. Its prime factorisation is × 7 × 673. Divisors (16): 1, 2, 4, 7, 8, 14, 28, 56, 673, 1346, 2692, 4711, 5384, 9422, 18844, 37688.
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How to work it out
- 1
37688 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
- 2
37688 is composite. Its prime factorisation is
- 3
The divisors add up to 80880; without 37688 itself that is 43192, so 37688 is abundant (43192 is more than 37688). Euler's totient φ(37688) = 16128 numbers up to 37688 share no factor with it.
- 4
The digits of 37688 add up to 32, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 62 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37688 = 2^{3} \times 7 \times 673 \]37688 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 80880 |
| Euler totient φ(n) | 16128 |
| Square | 1420385344 |
| Cube | 53531482844672 |
| Square root | 194.133974 (= 2√9422) |
| Digit sum / digital root | 32 / 5 |
| Collatz steps to 1 | 62 |
| Scientific notation | 3.7688 × |
37688 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand six hundred and eighty-eight |
| Binary (base 2) | 1001001100111000 |
| Octal (base 8) | 111470 |
| Hexadecimal (base 16) | 9338 |
| Base 3 | 1220200212 |
| As time | 37688 seconds = 10 h 28 min 8 s |
Is 37688 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37688 ÷ 2 = 18844) | 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 (37688 ÷ 4 = 9422) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | 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 | Yes (37688 ÷ 7 = 5384) | 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 (37688 ÷ 8 = 4711) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | 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 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37688 a prime number?
No. 37688 = × 7 × 673, so it is divisible by 2.
What are the factors of 37688?
1, 2, 4, 7, 8, 14, 28, 56, 673, 1346, 2692, 4711, 5384, 9422, 18844, 37688.
What is 37688 in binary?
1001001100111000 (hexadecimal 9338, octal 111470).
What is the square root of 37688?
About 194.1340, exactly 2√9422.
Is 37688 divisible by 3?
No. Its digits add up to 32, which is not a multiple of 3.
What is special about the number 37688?
It is a composite number with 16 divisors.