465
465 is a odd composite number that follows 464 and precedes 466. It is composed of 8 distinct factors: 1, 3, 5, 15, 31, 93, 155, 465. Its prime factorization can be written as 3 × 5 × 31. 465 is classified as a deficient number based on the sum of its proper divisors. In computer science, 465 is represented as 111010001 in binary and 1D1 in hexadecimal. Historically, it is written as CDLXV in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
8 FactorsProperties
The prime factorization (3 × 5 × 31) reveals 3 prime building blocks.
Divisible by 2
465 ends in 5, so it is odd.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 65 are not divisible by 4.
Divisible by 5
465 ends in 5, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 15 is not a multiple of 9.
Divisible by 10
465 does not end in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Deficient classification and digit analytics place 465 within several notable number theory sequences:
Timeline
Deep dive
How 465 breaks down
465 carries 8 distinct factors and a digit signature of 15 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 303, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111010001 supports bitwise reasoning, hexadecimal 1D1 aligns with computing notation, and the Roman numeral CDLXV keeps the encyclopedic tradition alive. These attributes make 465 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 465 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (460–470) to tune search ranges, and educators feature 465 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, Deficient numbers, Triangular numbers) help historians, numerologists, and trivia writers tie 465 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 465
Is 465 a prime number?
465 is composite with 8 total factors and the prime factorization 3 × 5 × 31.
What is the prime factorization of 465?
It breaks down as 3 × 5 × 31, multiplying the primes 3 × 5 × 31.
How is 465 represented in binary and hexadecimal?
465 converts to 111010001 in binary and 1D1 in hexadecimal, which are helpful for computer science applications.
Is 465 a perfect square, cube, or triangular number?
465 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 465?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.