113
113 is a odd prime number that follows 112 and precedes 114. As a prime number, 113 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 113. 113 is classified as a deficient number based on the sum of its proper divisors. In computer science, 113 is represented as 1110001 in binary and 71 in hexadecimal. Historically, it is written as CXIII in Roman numerals.
Factor Analysis
2 FactorsProperties
113 is prime, so its only factors are 1 and 113.
Divisible by 2
113 ends in 3, so it is odd.
Divisible by 3
The digit sum 5 is not a multiple of 3.
Divisible by 4
The last two digits 13 are not divisible by 4.
Divisible by 5
113 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 5 is not a multiple of 9.
Divisible by 10
113 does not end in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Deficient classification and digit analytics place 113 within several notable number theory sequences:
Timeline
Deep dive
How 113 breaks down
113 carries 2 distinct factors and a digit signature of 5 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 1, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1110001 supports bitwise reasoning, hexadecimal 71 aligns with computing notation, and the Roman numeral CXIII keeps the encyclopedic tradition alive. These attributes make 113 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 113 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (108–118) to tune search ranges, and educators feature 113 in worksheets about prime identification. 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 (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 113 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 113
Is 113 a prime number?
113 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 113?
113 is already prime, so the factorization is simply 113.
How is 113 represented in binary and hexadecimal?
113 converts to 1110001 in binary and 71 in hexadecimal, which are helpful for computer science applications.
Is 113 a perfect square, cube, or triangular number?
113 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 113?
The digits sum to 5, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.