The number 10112
10112 is a composite number with 16 divisors. Its prime factorisation is × 79. Divisors (16): 1, 2, 4, 8, 16, 32, 64, 79, 128, 158, 316, 632, 1264, 2528, 5056, 10112.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10112: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
10112 is composite. Its prime factorisation is
- 3
The divisors add up to 20400; without 10112 itself that is 10288, so 10112 is abundant (10288 is more than 10112). Euler's totient φ(10112) = 4992 numbers up to 10112 share no factor with it.
- 4
The digits of 10112 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 42 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10112 = 2^{7} \times 79 \]10112 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 20400 |
| Euler totient φ(n) | 4992 |
| Square | 102252544 |
| Cube | 1033977724928 |
| Square root | 100.558441 (= 8√158) |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 42 |
| Scientific notation | 1.0112 × |
10112 in other forms
| Form | Value |
|---|---|
| In words | ten thousand one hundred and twelve |
| Binary (base 2) | 10011110000000 |
| Octal (base 8) | 23600 |
| Hexadecimal (base 16) | 2780 |
| Base 3 | 111212112 |
| As time | 10112 seconds = 2 h 48 min 32 s |
Is 10112 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10112 ÷ 2 = 5056) | 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 (10112 ÷ 4 = 2528) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 2) | 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 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 | Yes (10112 ÷ 8 = 1264) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 2) | 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 8) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10112 a prime number?
No. 10112 = × 79, so it is divisible by 2.
What are the factors of 10112?
1, 2, 4, 8, 16, 32, 64, 79, 128, 158, 316, 632, 1264, 2528, 5056, 10112.
What is 10112 in binary?
10011110000000 (hexadecimal 2780, octal 23600).
What is the square root of 10112?
About 100.5584, exactly 8√158.
Is 10112 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 10112?
10112 is a happy number: repeatedly adding the squares of its digits reaches 1.