Number dictionary · Exact arithmetic
112: factors and number facts
one hundred twelve is an even number and is composite. Its 10 positive divisors form 5 factor pairs.
Number JD Editorial Team · Updated 2026-10-08
- In words
- one hundred twelve
- Roman numeral
- CXII
- Prime factorization
- 2^4 × 7
- Digital root
- 4
All factors of 112
A positive factor divides 112 with no remainder. In ascending order, the complete list is:
1, 2, 4, 7, 8, 14, 16, 28, 56, 112
Factor pairs
- 1 × 112 = 112
- 2 × 56 = 112
- 4 × 28 = 112
- 7 × 16 = 112
- 8 × 14 = 112
Each pair describes an arrangement of 112 items into equal rows. The pairs have different row and column counts; 112 cannot make a square array of whole items.
Divisor totals
- Positive divisors
- 10
- Sum of all divisors
- 248
- Sum excluding 112
- 136
- Classification
- abundant
112 is abundant because its proper divisors add to 136, which is greater than 112.
Prime factorization of 112
112 = 2^4 × 7
Repeated division, step by step
- 112 ÷ 2 = 56
- 56 ÷ 2 = 28
- 28 ÷ 2 = 14
- 14 ÷ 2 = 7
- 7 ÷ 7 = 1
Multiply the prime divisors in these steps to reconstruct 112. An exponent records how many times the same prime occurs. The divisor-count calculation is (4 + 1) × (1 + 1) = 10.
The preceding prime is 109. The next larger prime is 113. The factor list above explains why 112 is composite.
Learn the factorization method112 in words, Roman numerals and other bases
| Representation | Value |
|---|---|
| English (US style) | one hundred twelve |
| Roman numeral | CXII |
| Binary (base 2) | 1110000 |
| Octal (base 8) | 160 |
| Decimal (base 10) | 112 |
| Hexadecimal (base 16) | 70 |
Check the binary conversion
Read 1110000 from right to left using place values 1, 2, 4, 8 and successive powers of two. Keep the values whose bit is 1:
64 + 32 + 16 = 112
Check the hexadecimal conversion
7 × 16^1 + 0 × 16^0 = 112
Hexadecimal uses A through F for digit values 10 through 15. These notations represent the same quantity; changing the base does not change the integer.
Square, cube and square root of 112
- 112 squared
- 112 × 112 = 12,544
- 112 cubed
- 112 × 112 × 112 = 1,404,928
- Square root
- ≈ 10.583005
- Simplified radical
- 4√7
112 lies between 100 (10²) and 121 (11²), so it is not a perfect square. It is not a perfect cube.
112 is not triangular: no positive whole-number k satisfies k(k + 1) / 2 = 112.
Distinguish a square from a square rootMultiplication table for 112
These are the first twelve positive multiples. Unlike the finite factor list, the sequence of multiples continues without an upper limit.
Divisibility checks
| Divide by | Whole quotient | Remainder | Divides exactly? |
|---|---|---|---|
| 2 | 56 | 0 | Yes |
| 3 | 37 | 1 | No |
| 4 | 28 | 0 | Yes |
| 5 | 22 | 2 | No |
| 6 | 18 | 4 | No |
| 7 | 16 | 0 | Yes |
| 8 | 14 | 0 | Yes |
| 9 | 12 | 4 | No |
| 10 | 11 | 2 | No |
| 11 | 10 | 2 | No |
| 12 | 9 | 4 | No |
For example, 112 = 7 × 16 + 0. A remainder of zero is what makes a divisor a factor.
Digit sum and digital root of 112
112 contains 3 decimal digits. Its digit sum is 1 + 1 + 2 = 4.
- 112: 1 + 1 + 2 = 4
The digital root is 4. Reversing its digits gives 211; it is not a decimal palindrome. Digit patterns depend on the notation being used.
Digital-root arithmetic always finishes at a single digit for a positive integer. Some numerology methods stop at 11, 22 or 33 instead; that is a separate interpretive convention.
Fractions and a worked comparison
As a fraction of 100, 112/100 simplifies to 28/25 by dividing both terms by their greatest common divisor, 4. Its decimal value is 1.12. Because the numerator exceeds the denominator, this value is greater than one.
The greatest common divisor of 112 and 12 is 4. Their least common multiple is 336. The identity GCD × LCM = 112 × 12 = 1344 checks both results.
Work through GCF and LCMQuestions about 112
What are the factors of 112?
The positive factors are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112. There are 10 factors, including 1 and 112.
Is 112 a prime number?
No. 112 is composite: 2^4 × 7 = 112.
How do you write 112 in Roman numerals?
112 is CXII in standard subtractive Roman numeral notation.
What is the binary representation of 112?
112 in decimal is 1110000 in base 2. Adding its active place values gives 64 + 32 + 16 = 112.
Methods and reference definitions
Number JD calculates each result from the integer on this page. Positive factors are enumerated in pairs; repeated division gives the prime factorization; place values verify base conversions. Decimal square roots are rounded to six places when irrational.
NUMBER JOURNAL / JD
A reflective note on 112
Meaning varies by tradition and personal experience. One sighting is not evidence of what will happen next.
The digits of 112 add to 4. That arithmetic result is separate from the cultural symbolism of the pattern. If this number matters to you, write down what you noticed and choose one grounded action rather than treating the sighting as a prediction.