3600
3600 is a even composite number that follows 3599 and precedes 3601. It is composed of 45 distinct factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, 3600. Its prime factorization can be written as 2^4 × 3^2 × 5^2. 3600 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3600 is represented as 111000010000 in binary and E10 in hexadecimal. Historically, it is written as MMMDC in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
45 FactorsProperties
The prime factorization (2^4 × 3^2 × 5^2) reveals 8 prime building blocks.
Divisible by 2
3600 ends in 0, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
3600 ends in 0, so it is divisible by 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
3600 ends in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 3600 within several notable number theory sequences:
Timeline
Deep dive
How 3600 breaks down
3600 carries 45 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 8893, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111000010000 supports bitwise reasoning, hexadecimal E10 aligns with computing notation, and the Roman numeral MMMDC keeps the encyclopedic tradition alive. These attributes make 3600 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3600 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3595–3605) to tune search ranges, and educators feature 3600 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, Abundant numbers, Perfect squares) help historians, numerologists, and trivia writers tie 3600 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 3600
Is 3600 a prime number?
3600 is composite with 45 total factors and the prime factorization 2^4 × 3^2 × 5^2.
What is the prime factorization of 3600?
It breaks down as 2^4 × 3^2 × 5^2, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5.
How is 3600 represented in binary and hexadecimal?
3600 converts to 111000010000 in binary and E10 in hexadecimal, which are helpful for computer science applications.
Is 3600 a perfect square, cube, or triangular number?
3600 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3600?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.