The number 7986
7986 is a composite number with 16 divisors. Its prime factorisation is 2 × 3 × . Divisors (16): 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726, 1331, 2662, 3993, 7986.
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How to work it out
- 1
What is special about 7986: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
7986 is composite. Its prime factorisation is
- 3
The divisors add up to 17568; without 7986 itself that is 9582, so 7986 is abundant (9582 is more than 7986). Euler's totient φ(7986) = 2420 numbers up to 7986 share no factor with it.
- 4
The digits of 7986 add up to 30, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 7986 = 2 \times 3 \times 11^{3} \]7986 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 17568 |
| Euler totient φ(n) | 2420 |
| Square | 63776196 |
| Cube | 509316701256 |
| Square root | 89.364422 (= 11√66) |
| Digit sum / digital root | 30 / 3 |
| Collatz steps to 1 | 52 |
| Scientific notation | 7.986 × |
7986 in other forms
| Form | Value |
|---|---|
| In words | seven thousand nine hundred and eighty-six |
| Binary (base 2) | 1111100110010 |
| Octal (base 8) | 17462 |
| Hexadecimal (base 16) | 1F32 |
| Base 3 | 101221210 |
| As time | 7986 seconds = 2 h 13 min 6 s |
Is 7986 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (7986 ÷ 2 = 3993) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (7986 ÷ 3 = 2662) | 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 (7986 ÷ 6 = 1331) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | 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 3) | 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 | Yes (7986 ÷ 11 = 726) | 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 7986 a prime number?
No. 7986 = 2 × 3 × , so it is divisible by 2.
What are the factors of 7986?
1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726, 1331, 2662, 3993, 7986.
What is 7986 in binary?
1111100110010 (hexadecimal 1F32, octal 17462).
What is the square root of 7986?
About 89.3644, exactly 11√66.
Is 7986 divisible by 3?
Yes. Its digits add up to 30, a multiple of 3.
What is special about the number 7986?
7986 is a happy number: repeatedly adding the squares of its digits reaches 1.