468
468 is a even composite number that follows 467 and precedes 469. It is composed of 18 distinct factors: 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468. Its prime factorization can be written as 2^2 × 3^2 × 13. 468 is classified as a abundant number based on the sum of its proper divisors. In computer science, 468 is represented as 111010100 in binary and 1D4 in hexadecimal. Historically, it is written as CDLXVIII in Roman numerals.
Factor Analysis
18 FactorsProperties
The prime factorization (2^2 × 3^2 × 13) reveals 5 prime building blocks.
Divisible by 2
468 ends in 8, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 68 form a multiple of 4.
Divisible by 5
468 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 18 is a multiple of 9.
Divisible by 10
468 does not end in 0.
Divisible by 11
The alternating digit sum 6 is not a multiple of 11.
Abundant classification and digit analytics place 468 within several notable number theory sequences:
Timeline
Deep dive
How 468 breaks down
468 carries 18 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 806, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111010100 supports bitwise reasoning, hexadecimal 1D4 aligns with computing notation, and the Roman numeral CDLXVIII keeps the encyclopedic tradition alive. These attributes make 468 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 468 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (463–473) to tune search ranges, and educators feature 468 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 468 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 468
Is 468 a prime number?
468 is composite with 18 total factors and the prime factorization 2^2 × 3^2 × 13.
What is the prime factorization of 468?
It breaks down as 2^2 × 3^2 × 13, multiplying the primes 2 × 2 × 3 × 3 × 13.
How is 468 represented in binary and hexadecimal?
468 converts to 111010100 in binary and 1D4 in hexadecimal, which are helpful for computer science applications.
Is 468 a perfect square, cube, or triangular number?
468 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 468?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.