1005
1005 is a odd composite number that follows 1004 and precedes 1006. It is composed of 8 distinct factors: 1, 3, 5, 15, 67, 201, 335, 1005. Its prime factorization can be written as 3 × 5 × 67. 1005 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1005 is represented as 1111101101 in binary and 3ED in hexadecimal. Historically, it is written as MV in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (3 × 5 × 67) reveals 3 prime building blocks.
Divisible by 2
1005 ends in 5, so it is odd.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 05 are not divisible by 4.
Divisible by 5
1005 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 6 is not a multiple of 9.
Divisible by 10
1005 does not end in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Deficient classification and digit analytics place 1005 within several notable number theory sequences:
Timeline
Deep dive
How 1005 breaks down
1005 carries 8 distinct factors and a digit signature of 6 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 627, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111101101 supports bitwise reasoning, hexadecimal 3ED aligns with computing notation, and the Roman numeral MV keeps the encyclopedic tradition alive. These attributes make 1005 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1005 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1000–1010) to tune search ranges, and educators feature 1005 in worksheets about factor trees. 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 (Composite numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 1005 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 1005
Is 1005 a prime number?
1005 is composite with 8 total factors and the prime factorization 3 × 5 × 67.
What is the prime factorization of 1005?
It breaks down as 3 × 5 × 67, multiplying the primes 3 × 5 × 67.
How is 1005 represented in binary and hexadecimal?
1005 converts to 1111101101 in binary and 3ED in hexadecimal, which are helpful for computer science applications.
Is 1005 a perfect square, cube, or triangular number?
1005 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1005?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.