360
360 is a even composite number that follows 359 and precedes 361. It is composed of 24 distinct factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360. Its prime factorization can be written as 2^3 × 3^2 × 5. 360 is classified as a abundant number based on the sum of its proper divisors. In computer science, 360 is represented as 101101000 in binary and 168 in hexadecimal. Historically, it is written as CCCLX in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^3 × 3^2 × 5) reveals 6 prime building blocks.
Divisible by 2
360 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 60 form a multiple of 4.
Divisible by 5
360 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
360 ends in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 360 within several notable number theory sequences:
Timeline
Deep dive
How 360 breaks down
360 carries 24 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 810, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101101000 supports bitwise reasoning, hexadecimal 168 aligns with computing notation, and the Roman numeral CCCLX keeps the encyclopedic tradition alive. These attributes make 360 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 360 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (355–365) to tune search ranges, and educators feature 360 in worksheets about factor trees. Its binary footprint of length 9 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 360 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 360
Is 360 a prime number?
360 is composite with 24 total factors and the prime factorization 2^3 × 3^2 × 5.
What is the prime factorization of 360?
It breaks down as 2^3 × 3^2 × 5, multiplying the primes 2 × 2 × 2 × 3 × 3 × 5.
How is 360 represented in binary and hexadecimal?
360 converts to 101101000 in binary and 168 in hexadecimal, which are helpful for computer science applications.
Is 360 a perfect square, cube, or triangular number?
360 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 360?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.