4005
4005 is a odd composite number that follows 4004 and precedes 4006. It is composed of 12 distinct factors: 1, 3, 5, 9, 15, 45, 89, 267, 445, 801, 1335, 4005. Its prime factorization can be written as 3^2 × 5 × 89. 4005 is classified as a deficient number based on the sum of its proper divisors. In computer science, 4005 is represented as 111110100101 in binary and FA5 in hexadecimal. It also belongs to the triangular number sequence.
Factor Analysis
12 FactorsProperties
The prime factorization (3^2 × 5 × 89) reveals 4 prime building blocks.
Divisible by 2
4005 ends in 5, so it is odd.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 05 are not divisible by 4.
Divisible by 5
4005 ends in 5, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 9 is a multiple of 9.
Divisible by 10
4005 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 4005 within several notable number theory sequences:
Timeline
Deep dive
How 4005 breaks down
4005 carries 12 distinct factors and a digit signature of 9 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 3015, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111110100101 supports bitwise reasoning, hexadecimal FA5 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4005 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4005 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (4000–4010) to tune search ranges, and educators feature 4005 in worksheets about factor trees. 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 (Composite numbers, Deficient numbers, Triangular numbers) help historians, numerologists, and trivia writers tie 4005 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 4005
Is 4005 a prime number?
4005 is composite with 12 total factors and the prime factorization 3^2 × 5 × 89.
What is the prime factorization of 4005?
It breaks down as 3^2 × 5 × 89, multiplying the primes 3 × 3 × 5 × 89.
How is 4005 represented in binary and hexadecimal?
4005 converts to 111110100101 in binary and FA5 in hexadecimal, which are helpful for computer science applications.
Is 4005 a perfect square, cube, or triangular number?
4005 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 4005?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.