The number 10016
10016 is a composite number with 12 divisors. Its prime factorisation is × 313. Divisors (12): 1, 2, 4, 8, 16, 32, 313, 626, 1252, 2504, 5008, 10016.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10016: a Harshad number: divisible by its digit sum 8.
- 2
10016 is composite. Its prime factorisation is
- 3
The divisors add up to 19782; without 10016 itself that is 9766, so 10016 is deficient (9766 is less than 10016). Euler's totient φ(10016) = 4992 numbers up to 10016 share no factor with it.
- 4
The digits of 10016 add up to 8, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10016 = 2^{5} \times 313 \]10016 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 12 |
| Sum of divisors | 19782 |
| Euler totient φ(n) | 4992 |
| Square | 100320256 |
| Cube | 1004807684096 |
| Square root | 100.079968 (= 4√626) |
| Digit sum / digital root | 8 / 8 |
| Collatz steps to 1 | 135 |
| Scientific notation | 1.0016 × |
10016 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and sixteen |
| Binary (base 2) | 10011100100000 |
| Octal (base 8) | 23440 |
| Hexadecimal (base 16) | 2720 |
| Base 3 | 111201222 |
| As time | 10016 seconds = 2 h 46 min 56 s |
Is 10016 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10016 ÷ 2 = 5008) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10016 ÷ 4 = 2504) | 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 | No (remainder 2) | 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 | Yes (10016 ÷ 8 = 1252) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | 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 6) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10016 a prime number?
No. 10016 = × 313, so it is divisible by 2.
What are the factors of 10016?
1, 2, 4, 8, 16, 32, 313, 626, 1252, 2504, 5008, 10016.
What is 10016 in binary?
10011100100000 (hexadecimal 2720, octal 23440).
What is the square root of 10016?
About 100.0800, exactly 4√626.
Is 10016 divisible by 3?
No. Its digits add up to 8, which is not a multiple of 3.
What is special about the number 10016?
10016 is a Harshad number: divisible by its digit sum 8.