462
462 is a even composite number that follows 461 and precedes 463. It is composed of 16 distinct factors: 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462. Its prime factorization can be written as 2 × 3 × 7 × 11. 462 is classified as a abundant number based on the sum of its proper divisors. In computer science, 462 is represented as 111001110 in binary and 1CE in hexadecimal. Historically, it is written as CDLXII in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2 × 3 × 7 × 11) reveals 4 prime building blocks.
Divisible by 2
462 ends in 2, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 62 are not divisible by 4.
Divisible by 5
462 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
462 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 462 within several notable number theory sequences:
Timeline
Deep dive
How 462 breaks down
462 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 690, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111001110 supports bitwise reasoning, hexadecimal 1CE aligns with computing notation, and the Roman numeral CDLXII keeps the encyclopedic tradition alive. These attributes make 462 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 462 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (457–467) to tune search ranges, and educators feature 462 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 462 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 462
Is 462 a prime number?
462 is composite with 16 total factors and the prime factorization 2 × 3 × 7 × 11.
What is the prime factorization of 462?
It breaks down as 2 × 3 × 7 × 11, multiplying the primes 2 × 3 × 7 × 11.
How is 462 represented in binary and hexadecimal?
462 converts to 111001110 in binary and 1CE in hexadecimal, which are helpful for computer science applications.
Is 462 a perfect square, cube, or triangular number?
462 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 462?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.