991
991 is a odd prime number that follows 990 and precedes 992. As a prime number, 991 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 991. 991 is classified as a deficient number based on the sum of its proper divisors. In computer science, 991 is represented as 1111011111 in binary and 3DF in hexadecimal. Historically, it is written as CMXCI in Roman numerals.
Factor Analysis
2 FactorsProperties
991 is prime, so its only factors are 1 and 991.
Divisible by 2
991 ends in 1, so it is odd.
Divisible by 3
The digit sum 19 is not a multiple of 3.
Divisible by 4
The last two digits 91 are not divisible by 4.
Divisible by 5
991 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 19 is not a multiple of 9.
Divisible by 10
991 does not end in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Deficient classification and digit analytics place 991 within several notable number theory sequences:
Timeline
Deep dive
How 991 breaks down
991 carries 2 distinct factors and a digit signature of 19 (1 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 1111011111 supports bitwise reasoning, hexadecimal 3DF aligns with computing notation, and the Roman numeral CMXCI keeps the encyclopedic tradition alive. These attributes make 991 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 991 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (986–996) to tune search ranges, and educators feature 991 in worksheets about prime identification. Its binary footprint of length 10 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 991 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 991
Is 991 a prime number?
991 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 991?
991 is already prime, so the factorization is simply 991.
How is 991 represented in binary and hexadecimal?
991 converts to 1111011111 in binary and 3DF in hexadecimal, which are helpful for computer science applications.
Is 991 a perfect square, cube, or triangular number?
991 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 991?
The digits sum to 19, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.