3465
3465 is a odd composite number that follows 3464 and precedes 3466. It is composed of 24 distinct factors: 1, 3, 5, 7, 9, 11, 15, 21, 33, 35, 45, 55, 63, 77, 99, 105, 165, 231, 315, 385, 495, 693, 1155, 3465. Its prime factorization can be written as 3^2 × 5 × 7 × 11. 3465 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3465 is represented as 110110001001 in binary and D89 in hexadecimal. Historically, it is written as MMMCDLXV in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (3^2 × 5 × 7 × 11) reveals 5 prime building blocks.
Divisible by 2
3465 ends in 5, so it is odd.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 65 are not divisible by 4.
Divisible by 5
3465 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 18 is a multiple of 9.
Divisible by 10
3465 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Abundant classification and digit analytics place 3465 within several notable number theory sequences:
Timeline
Deep dive
How 3465 breaks down
3465 carries 24 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 4023, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110110001001 supports bitwise reasoning, hexadecimal D89 aligns with computing notation, and the Roman numeral MMMCDLXV keeps the encyclopedic tradition alive. These attributes make 3465 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3465 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3460–3470) to tune search ranges, and educators feature 3465 in worksheets about factor trees. Its binary footprint of length 12 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 3465 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 3465
Is 3465 a prime number?
3465 is composite with 24 total factors and the prime factorization 3^2 × 5 × 7 × 11.
What is the prime factorization of 3465?
It breaks down as 3^2 × 5 × 7 × 11, multiplying the primes 3 × 3 × 5 × 7 × 11.
How is 3465 represented in binary and hexadecimal?
3465 converts to 110110001001 in binary and D89 in hexadecimal, which are helpful for computer science applications.
Is 3465 a perfect square, cube, or triangular number?
3465 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3465?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.