4003
4003 is a odd prime number that follows 4002 and precedes 4004. As a prime number, 4003 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 4003. 4003 is classified as a deficient number based on the sum of its proper divisors. In computer science, 4003 is represented as 111110100011 in binary and FA3 in hexadecimal.
Factor Analysis
2 FactorsProperties
4003 is prime, so its only factors are 1 and 4003.
Divisible by 2
4003 ends in 3, so it is odd.
Divisible by 3
The digit sum 7 is not a multiple of 3.
Divisible by 4
The last two digits 03 are not divisible by 4.
Divisible by 5
4003 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 7 is not a multiple of 9.
Divisible by 10
4003 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 4003 within several notable number theory sequences:
Timeline
Deep dive
How 4003 breaks down
4003 carries 2 distinct factors and a digit signature of 7 (7 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 111110100011 supports bitwise reasoning, hexadecimal FA3 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4003 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4003 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3998–4008) to tune search ranges, and educators feature 4003 in worksheets about prime identification. Its binary footprint of length 12 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 4003 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 4003
Is 4003 a prime number?
4003 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 4003?
4003 is already prime, so the factorization is simply 4003.
How is 4003 represented in binary and hexadecimal?
4003 converts to 111110100011 in binary and FA3 in hexadecimal, which are helpful for computer science applications.
Is 4003 a perfect square, cube, or triangular number?
4003 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 4003?
The digits sum to 7, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.