1009
1009 is a odd prime number that follows 1008 and precedes 1010. As a prime number, 1009 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 1009. 1009 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1009 is represented as 1111110001 in binary and 3F1 in hexadecimal. Historically, it is written as MIX in Roman numerals.
Factor Analysis
2 FactorsProperties
1009 is prime, so its only factors are 1 and 1009.
Divisible by 2
1009 ends in 9, so it is odd.
Divisible by 3
The digit sum 10 is not a multiple of 3.
Divisible by 4
The last two digits 09 are not divisible by 4.
Divisible by 5
1009 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
1009 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 1009 within several notable number theory sequences:
Timeline
Deep dive
How 1009 breaks down
1009 carries 2 distinct factors and a digit signature of 10 (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 1111110001 supports bitwise reasoning, hexadecimal 3F1 aligns with computing notation, and the Roman numeral MIX keeps the encyclopedic tradition alive. These attributes make 1009 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1009 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1004–1014) to tune search ranges, and educators feature 1009 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 1009 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 1009
Is 1009 a prime number?
1009 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 1009?
1009 is already prime, so the factorization is simply 1009.
How is 1009 represented in binary and hexadecimal?
1009 converts to 1111110001 in binary and 3F1 in hexadecimal, which are helpful for computer science applications.
Is 1009 a perfect square, cube, or triangular number?
1009 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1009?
The digits sum to 10, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.