264
264 is a even composite number that follows 263 and precedes 265. It is composed of 16 distinct factors: 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264. Its prime factorization can be written as 2^3 × 3 × 11. 264 is classified as a abundant number based on the sum of its proper divisors. In computer science, 264 is represented as 100001000 in binary and 108 in hexadecimal. Historically, it is written as CCLXIV in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 3 × 11) reveals 5 prime building blocks.
Divisible by 2
264 ends in 4, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
264 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 12 is not a multiple of 9.
Divisible by 10
264 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 264 within several notable number theory sequences:
Timeline
Deep dive
How 264 breaks down
264 carries 16 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 456, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100001000 supports bitwise reasoning, hexadecimal 108 aligns with computing notation, and the Roman numeral CCLXIV keeps the encyclopedic tradition alive. These attributes make 264 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 264 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (259–269) to tune search ranges, and educators feature 264 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 264 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 264
Is 264 a prime number?
264 is composite with 16 total factors and the prime factorization 2^3 × 3 × 11.
What is the prime factorization of 264?
It breaks down as 2^3 × 3 × 11, multiplying the primes 2 × 2 × 2 × 3 × 11.
How is 264 represented in binary and hexadecimal?
264 converts to 100001000 in binary and 108 in hexadecimal, which are helpful for computer science applications.
Is 264 a perfect square, cube, or triangular number?
264 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 264?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.