1008
1008 is a even composite number that follows 1007 and precedes 1009. It is composed of 30 distinct factors: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008. Its prime factorization can be written as 2^4 × 3^2 × 7. 1008 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1008 is represented as 1111110000 in binary and 3F0 in hexadecimal. Historically, it is written as MVIII in Roman numerals.
Factor Analysis
30 FactorsProperties
The prime factorization (2^4 × 3^2 × 7) reveals 7 prime building blocks.
Divisible by 2
1008 ends in 8, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 08 form a multiple of 4.
Divisible by 5
1008 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 9 is a multiple of 9.
Divisible by 10
1008 does not end in 0.
Divisible by 11
The alternating digit sum -7 is not a multiple of 11.
Abundant classification and digit analytics place 1008 within several notable number theory sequences:
Timeline
Deep dive
How 1008 breaks down
1008 carries 30 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 2216, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111110000 supports bitwise reasoning, hexadecimal 3F0 aligns with computing notation, and the Roman numeral MVIII keeps the encyclopedic tradition alive. These attributes make 1008 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1008 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1003–1013) to tune search ranges, and educators feature 1008 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, Abundant numbers) help historians, numerologists, and trivia writers tie 1008 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 1008
Is 1008 a prime number?
1008 is composite with 30 total factors and the prime factorization 2^4 × 3^2 × 7.
What is the prime factorization of 1008?
It breaks down as 2^4 × 3^2 × 7, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3 × 7.
How is 1008 represented in binary and hexadecimal?
1008 converts to 1111110000 in binary and 3F0 in hexadecimal, which are helpful for computer science applications.
Is 1008 a perfect square, cube, or triangular number?
1008 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1008?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.