The number 10116
10116 is a composite number with 18 divisors. Its prime factorisation is × × 281. Divisors (18): 1, 2, 3, 4, 6, 9, 12, 18, 36, 281, 562, 843, 1124, 1686, 2529, 3372 … 10116.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10116: a Harshad number: divisible by its digit sum 9.
- 2
10116 is composite. Its prime factorisation is
- 3
The divisors add up to 25662; without 10116 itself that is 15546, so 10116 is abundant (15546 is more than 10116). Euler's totient φ(10116) = 3360 numbers up to 10116 share no factor with it.
- 4
The digits of 10116 add up to 9, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 73 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10116 = 2^{2} \times 3^{2} \times 281 \]10116 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 18 |
| Sum of divisors | 25662 |
| Euler totient φ(n) | 3360 |
| Square | 102333456 |
| Cube | 1035205240896 |
| Square root | 100.578328 (= 6√281) |
| Digit sum / digital root | 9 / 9 |
| Collatz steps to 1 | 73 |
| Scientific notation | 1.0116 × |
10116 in other forms
| Form | Value |
|---|---|
| In words | ten thousand one hundred and sixteen |
| Binary (base 2) | 10011110000100 |
| Octal (base 8) | 23604 |
| Hexadecimal (base 16) | 2784 |
| Base 3 | 111212200 |
| As time | 10116 seconds = 2 h 48 min 36 s |
Is 10116 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10116 ÷ 2 = 5058) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (10116 ÷ 3 = 3372) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10116 ÷ 4 = 2529) | 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 (10116 ÷ 6 = 1686) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 1) | 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 (10116 ÷ 9 = 1124) | 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 7) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (10116 ÷ 12 = 843) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10116 a prime number?
No. 10116 = × × 281, so it is divisible by 2.
What are the factors of 10116?
1, 2, 3, 4, 6, 9, 12, 18, 36, 281, 562, 843, 1124, 1686, 2529, 3372, 5058, 10116.
What is 10116 in binary?
10011110000100 (hexadecimal 2784, octal 23604).
What is the square root of 10116?
About 100.5783, exactly 6√281.
Is 10116 divisible by 3?
Yes. Its digits add up to 9, a multiple of 3.
What is special about the number 10116?
10116 is a Harshad number: divisible by its digit sum 9.