464
464 is a even composite number that follows 463 and precedes 465. It is composed of 10 distinct factors: 1, 2, 4, 8, 16, 29, 58, 116, 232, 464. Its prime factorization can be written as 2^4 × 29. 464 is classified as a abundant number based on the sum of its proper divisors. In computer science, 464 is represented as 111010000 in binary and 1D0 in hexadecimal. Historically, it is written as CDLXIV in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 29) reveals 5 prime building blocks.
Divisible by 2
464 ends in 4, so it is even.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
464 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 14 is not a multiple of 9.
Divisible by 10
464 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 464 within several notable number theory sequences:
Timeline
Deep dive
How 464 breaks down
464 carries 10 distinct factors and a digit signature of 14 (5 as the digital root). The abundant classification indicates that its proper divisors sum to 466, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111010000 supports bitwise reasoning, hexadecimal 1D0 aligns with computing notation, and the Roman numeral CDLXIV keeps the encyclopedic tradition alive. These attributes make 464 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 464 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (459–469) to tune search ranges, and educators feature 464 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 464 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 464
Is 464 a prime number?
464 is composite with 10 total factors and the prime factorization 2^4 × 29.
What is the prime factorization of 464?
It breaks down as 2^4 × 29, multiplying the primes 2 × 2 × 2 × 2 × 29.
How is 464 represented in binary and hexadecimal?
464 converts to 111010000 in binary and 1D0 in hexadecimal, which are helpful for computer science applications.
Is 464 a perfect square, cube, or triangular number?
464 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 464?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.