The number 65988
65988 is a composite number with 48 divisors. Its prime factorisation is × × 13 × 47. Divisors (48): 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 47, 52, 54 … 65988.
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How to work it out
- 1
What is special about 65988: a Harshad number: divisible by its digit sum 36.
- 2
65988 is composite. Its prime factorisation is
- 3
The divisors add up to 188160; without 65988 itself that is 122172, so 65988 is abundant (122172 is more than 65988). Euler's totient φ(65988) = 19872 numbers up to 65988 share no factor with it.
- 4
The digits of 65988 add up to 36, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 130 steps to reach 1.
LaTeX source of the formulas on this page
\[ 65988 = 2^{2} \times 3^{3} \times 13 \times 47 \]65988 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 48 |
| Sum of divisors | 188160 |
| Euler totient φ(n) | 19872 |
| Square | 4354416144 |
| Cube | 287339212510272 |
| Square root | 256.881296 (= 6√1833) |
| Digit sum / digital root | 36 / 9 |
| Collatz steps to 1 | 130 |
| Scientific notation | 6.5988 × |
65988 in other forms
| Form | Value |
|---|---|
| In words | sixty-five thousand nine hundred and eighty-eight |
| Binary (base 2) | 10000000111000100 |
| Octal (base 8) | 200704 |
| Hexadecimal (base 16) | 101C4 |
| Base 3 | 10100112000 |
| As time | 65988 seconds = 18 h 19 min 48 s |
Is 65988 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (65988 ÷ 2 = 32994) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (65988 ÷ 3 = 21996) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (65988 ÷ 4 = 16497) | 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 (65988 ÷ 6 = 10998) | 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 4) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (65988 ÷ 9 = 7332) | 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 10) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (65988 ÷ 12 = 5499) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 65988 a prime number?
No. 65988 = × × 13 × 47, so it is divisible by 2.
What are the factors of 65988?
1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 47, 52, 54, 78, 94, 108, 117, 141, 156, 188, 234, 282, 351, 423, 468, 564, 611, 702, 846, 1222, 1269, 1404, 1692, 1833, 2444, 2538, 3666, 5076, 5499, 7332, 10998, 16497, 21996, 32994, 65988.
What is 65988 in binary?
10000000111000100 (hexadecimal 101C4, octal 200704).
What is the square root of 65988?
About 256.8813, exactly 6√1833.
Is 65988 divisible by 3?
Yes. Its digits add up to 36, a multiple of 3.
What is special about the number 65988?
65988 is a Harshad number: divisible by its digit sum 36.