4007
4007 is a odd prime number that follows 4006 and precedes 4008. As a prime number, 4007 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 4007. 4007 is classified as a deficient number based on the sum of its proper divisors. In computer science, 4007 is represented as 111110100111 in binary and FA7 in hexadecimal.
Factor Analysis
2 FactorsProperties
4007 is prime, so its only factors are 1 and 4007.
Divisible by 2
4007 ends in 7, so it is odd.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 07 are not divisible by 4.
Divisible by 5
4007 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 11 is not a multiple of 9.
Divisible by 10
4007 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 4007 within several notable number theory sequences:
Timeline
Deep dive
How 4007 breaks down
4007 carries 2 distinct factors and a digit signature of 11 (2 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 111110100111 supports bitwise reasoning, hexadecimal FA7 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4007 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4007 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (4002–4012) to tune search ranges, and educators feature 4007 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 4007 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 4007
Is 4007 a prime number?
4007 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 4007?
4007 is already prime, so the factorization is simply 4007.
How is 4007 represented in binary and hexadecimal?
4007 converts to 111110100111 in binary and FA7 in hexadecimal, which are helpful for computer science applications.
Is 4007 a perfect square, cube, or triangular number?
4007 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 4007?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.