The number 37986
37986 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × 13 × 487. Divisors (16): 1, 2, 3, 6, 13, 26, 39, 78, 487, 974, 1461, 2922, 6331, 12662, 18993, 37986.
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How to work it out
- 1
What is special about 37986: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
37986 is composite. Its prime factorisation is
- 3
The divisors add up to 81984; without 37986 itself that is 43998, so 37986 is abundant (43998 is more than 37986). Euler's totient φ(37986) = 11664 numbers up to 37986 share no factor with it.
- 4
The digits of 37986 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 54 steps to reach 1.
LaTeX source of the formulas on this page
\[ 37986 = 2 \times 3 \times 13 \times 487 \]
37986 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 81984 |
| Euler totient φ(n) | 11664 |
| Square | 1442936196 |
| Cube | 54811374341256 |
| Square root | 194.899974 |
| Digit sum / digital root | 33 / 6 |
| Collatz steps to 1 | 54 |
| Scientific notation | 3.7986 × |
37986 in other forms
| Form | Value |
|---|---|
| In words | thirty-seven thousand nine hundred and eighty-six |
| Binary (base 2) | 1001010001100010 |
| Octal (base 8) | 112142 |
| Hexadecimal (base 16) | 9462 |
| Base 3 | 1221002220 |
| As time | 37986 seconds = 10 h 33 min 6 s |
Is 37986 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (37986 ÷ 2 = 18993) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (37986 ÷ 3 = 12662) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 2) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (37986 ÷ 6 = 6331) | 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 | No (remainder 2) | 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 6) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 6) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 37986 a prime number?
No. 37986 = 2 × 3 × 13 × 487, so it is divisible by 2.
What are the factors of 37986?
1, 2, 3, 6, 13, 26, 39, 78, 487, 974, 1461, 2922, 6331, 12662, 18993, 37986.
What is 37986 in binary?
1001010001100010 (hexadecimal 9462, octal 112142).
What is the square root of 37986?
About 194.9000.
Is 37986 divisible by 3?
Yes. Its digits add up to 33, a multiple of 3.
What is special about the number 37986?
37986 is a happy number: repeatedly adding the squares of its digits reaches 1.