1608
1608 is a even composite number that follows 1607 and precedes 1609. It is composed of 16 distinct factors: 1, 2, 3, 4, 6, 8, 12, 24, 67, 134, 201, 268, 402, 536, 804, 1608. Its prime factorization can be written as 2^3 × 3 × 67. 1608 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1608 is represented as 11001001000 in binary and 648 in hexadecimal. Historically, it is written as MDCVIII in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 3 × 67) reveals 5 prime building blocks.
Divisible by 2
1608 ends in 8, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 08 form a multiple of 4.
Divisible by 5
1608 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 15 is not a multiple of 9.
Divisible by 10
1608 does not end in 0.
Divisible by 11
The alternating digit sum -13 is not a multiple of 11.
Abundant classification and digit analytics place 1608 within several notable number theory sequences:
Timeline
Deep dive
How 1608 breaks down
1608 carries 16 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 2472, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11001001000 supports bitwise reasoning, hexadecimal 648 aligns with computing notation, and the Roman numeral MDCVIII keeps the encyclopedic tradition alive. These attributes make 1608 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1608 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1603–1613) to tune search ranges, and educators feature 1608 in worksheets about factor trees. Its binary footprint of length 11 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 1608 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 1608
Is 1608 a prime number?
1608 is composite with 16 total factors and the prime factorization 2^3 × 3 × 67.
What is the prime factorization of 1608?
It breaks down as 2^3 × 3 × 67, multiplying the primes 2 × 2 × 2 × 3 × 67.
How is 1608 represented in binary and hexadecimal?
1608 converts to 11001001000 in binary and 648 in hexadecimal, which are helpful for computer science applications.
Is 1608 a perfect square, cube, or triangular number?
1608 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1608?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.