91
91 is a odd composite number that follows 90 and precedes 92. It is composed of 4 distinct factors: 1, 7, 13, 91. Its prime factorization can be written as 7 × 13. 91 is classified as a deficient number based on the sum of its proper divisors. In computer science, 91 is represented as 1011011 in binary and 5B in hexadecimal. Historically, it is written as XCI in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
4 FactorsProperties
The prime factorization (7 × 13) reveals 2 prime building blocks.
Divisible by 2
91 ends in 1, so it is odd.
Divisible by 3
The digit sum 10 is not a multiple of 3.
Divisible by 4
The last two digits 91 are not divisible by 4.
Divisible by 5
91 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 10 is not a multiple of 9.
Divisible by 10
91 does not end in 0.
Divisible by 11
The alternating digit sum 8 is not a multiple of 11.
Deficient classification and digit analytics place 91 within several notable number theory sequences:
Timeline
Deep dive
How 91 breaks down
91 carries 4 distinct factors and a digit signature of 10 (1 as the digital root). The deficient classification indicates that its proper divisors sum to 21, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1011011 supports bitwise reasoning, hexadecimal 5B aligns with computing notation, and the Roman numeral XCI keeps the encyclopedic tradition alive. These attributes make 91 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 91 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (86–96) to tune search ranges, and educators feature 91 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, Deficient numbers, Triangular numbers) help historians, numerologists, and trivia writers tie 91 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 91
Is 91 a prime number?
91 is composite with 4 total factors and the prime factorization 7 × 13.
What is the prime factorization of 91?
It breaks down as 7 × 13, multiplying the primes 7 × 13.
How is 91 represented in binary and hexadecimal?
91 converts to 1011011 in binary and 5B in hexadecimal, which are helpful for computer science applications.
Is 91 a perfect square, cube, or triangular number?
91 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 91?
The digits sum to 10, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.