364
364 is a even composite number that follows 363 and precedes 365. It is composed of 12 distinct factors: 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364. Its prime factorization can be written as 2^2 × 7 × 13. 364 is classified as a abundant number based on the sum of its proper divisors. In computer science, 364 is represented as 101101100 in binary and 16C in hexadecimal. Historically, it is written as CCCLXIV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 7 × 13) reveals 4 prime building blocks.
Divisible by 2
364 ends in 4, so it is even.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
364 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 13 is not a multiple of 9.
Divisible by 10
364 does not end in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Abundant classification and digit analytics place 364 within several notable number theory sequences:
Timeline
Deep dive
How 364 breaks down
364 carries 12 distinct factors and a digit signature of 13 (4 as the digital root). The abundant classification indicates that its proper divisors sum to 420, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101101100 supports bitwise reasoning, hexadecimal 16C aligns with computing notation, and the Roman numeral CCCLXIV keeps the encyclopedic tradition alive. These attributes make 364 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 364 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (359–369) to tune search ranges, and educators feature 364 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 364 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 364
Is 364 a prime number?
364 is composite with 12 total factors and the prime factorization 2^2 × 7 × 13.
What is the prime factorization of 364?
It breaks down as 2^2 × 7 × 13, multiplying the primes 2 × 2 × 7 × 13.
How is 364 represented in binary and hexadecimal?
364 converts to 101101100 in binary and 16C in hexadecimal, which are helpful for computer science applications.
Is 364 a perfect square, cube, or triangular number?
364 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 364?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.