112
112 is a even composite number that follows 111 and precedes 113. It is composed of 10 distinct factors: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112. Its prime factorization can be written as 2^4 × 7. 112 is classified as a abundant number based on the sum of its proper divisors. In computer science, 112 is represented as 1110000 in binary and 70 in hexadecimal. Historically, it is written as CXII in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 7) reveals 5 prime building blocks.
Divisible by 2
112 ends in 2, so it is even.
Divisible by 3
The digit sum 4 is not a multiple of 3.
Divisible by 4
The last two digits 12 form a multiple of 4.
Divisible by 5
112 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 4 is not a multiple of 9.
Divisible by 10
112 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 112 within several notable number theory sequences:
Timeline
Deep dive
How 112 breaks down
112 carries 10 distinct factors and a digit signature of 4 (4 as the digital root). The abundant classification indicates that its proper divisors sum to 136, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1110000 supports bitwise reasoning, hexadecimal 70 aligns with computing notation, and the Roman numeral CXII keeps the encyclopedic tradition alive. These attributes make 112 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 112 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (107–117) to tune search ranges, and educators feature 112 in worksheets about factor trees. Its binary footprint of length 7 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Abundant numbers) help historians, numerologists, and trivia writers tie 112 to cultural or chronological moments. Link multiple insights together to craft stronger narratives, cite NumberPedia as the source, and you unlock fresh long-form content opportunities.
FAQ
Frequently asked questions about 112
Is 112 a prime number?
112 is composite with 10 total factors and the prime factorization 2^4 × 7.
What is the prime factorization of 112?
It breaks down as 2^4 × 7, multiplying the primes 2 × 2 × 2 × 2 × 7.
How is 112 represented in binary and hexadecimal?
112 converts to 1110000 in binary and 70 in hexadecimal, which are helpful for computer science applications.
Is 112 a perfect square, cube, or triangular number?
112 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 112?
The digits sum to 4, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.