The number 37968
37968 is a composite number with 40 divisors. Its prime factorisation is × 3 × 7 × 113. Divisors (40): 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56 … 37968.
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How to work it out
- 1
What is special about 37968: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
37968 is composite. Its prime factorisation is
- 3
The divisors add up to 113088; without 37968 itself that is 75120, so 37968 is abundant (75120 is more than 37968). Euler's totient φ(37968) = 10752 numbers up to 37968 share no factor with it.
- 4
The digits of 37968 add up to 33, and repeating that until one digit is left gives the digital root 6. The Collatz sequence (halve if even, else 3n+1) takes 80 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37968 = 2^{4} \times 3 \times 7 \times 113 \]37968 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 40 |
| Sum of divisors | 113088 |
| Euler totient φ(n) | 10752 |
| Square | 1441569024 |
| Cube | 54733492703232 |
| Square root | 194.853791 (= 4√2373) |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 80 |
| Scientific notation | 3.7968 × |
37968 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand nine hundred and sixty-eight |
| Binary (base 2) | 1001010001010000 |
| Octal (base 8) | 112120 |
| Hexadecimal (base 16) | 9450 |
| Base 3 | 1221002020 |
| As time | 37968 seconds = 10 h 32 min 48 s |
Is 37968 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37968 ÷ 2 = 18984) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37968 ÷ 3 = 12656) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (37968 ÷ 4 = 9492) | 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 | Yes (37968 ÷ 6 = 6328) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (37968 ÷ 7 = 5424) | 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 (37968 ÷ 8 = 4746) | 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 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (37968 ÷ 12 = 3164) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37968 a prime number?
No. 37968 = × 3 × 7 × 113, so it is divisible by 2.
What are the factors of 37968?
1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 113, 168, 226, 336, 339, 452, 678, 791, 904, 1356, 1582, 1808, 2373, 2712, 3164, 4746, 5424, 6328, 9492, 12656, 18984, 37968.
What is 37968 in binary?
1001010001010000 (hexadecimal 9450, octal 112120).
What is the square root of 37968?
About 194.8538, exactly 4√2373.
Is 37968 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 37968?
37968 is a happy number: repeatedly adding the squares of its digits reaches 1.