The number 112
112 is a composite number with 10 divisors. Its prime factorisation is × 7. Divisors (10): 1, 2, 4, 7, 8, 14, 16, 28, 56, 112.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 112: a Harshad number: divisible by its digit sum 4.
- 2
112 is composite. Its prime factorisation is
- 3
The divisors add up to 248; without 112 itself that is 136, so 112 is abundant (136 is more than 112). Euler's totient φ(112) = 48 numbers up to 112 share no factor with it.
- 4
The digits of 112 add up to 4, and repeating that until one digit is left gives the digital root 4. The Collatz sequence (halve if even, else 3n+1) takes 20 steps to reach 1.
LaTeX source of the formulas on this page
\[ 112 = 2^{4} \times 7 \]112 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 10 |
| Sum of divisors | 248 |
| Euler totient φ(n) | 48 |
| Square | 12544 |
| Cube | 1404928 |
| Square root | 10.583005 (= 4√7) |
| Digit sum / digital root | 4 / 4 |
| Collatz steps to 1 | 20 |
| Scientific notation | 1.12 × |
112 in other forms
| Form | Value |
|---|---|
| In words | one hundred and twelve |
| Roman numerals | CXII |
| Binary (base 2) | 1110000 |
| Octal (base 8) | 160 |
| Hexadecimal (base 16) | 70 |
| Base 3 | 11011 |
| As time | 112 seconds = 1 min 52 s |
Is 112 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (112 ÷ 2 = 56) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (112 ÷ 4 = 28) | 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 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (112 ÷ 7 = 16) | 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 (112 ÷ 8 = 14) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 4) | 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 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 112 a prime number?
No. 112 = × 7, so it is divisible by 2.
What are the factors of 112?
1, 2, 4, 7, 8, 14, 16, 28, 56, 112.
What is 112 in binary?
1110000 (hexadecimal 70, octal 160).
What is the square root of 112?
About 10.5830, exactly 4√7.
What is 112 in Roman numerals?
CXII.
Is 112 divisible by 3?
No. Its digits add up to 4, which is not a multiple of 3.
What is special about the number 112?
112 is a Harshad number: divisible by its digit sum 4.