3460
3460 is a even composite number that follows 3459 and precedes 3461. It is composed of 12 distinct factors: 1, 2, 4, 5, 10, 20, 173, 346, 692, 865, 1730, 3460. Its prime factorization can be written as 2^2 × 5 × 173. 3460 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3460 is represented as 110110000100 in binary and D84 in hexadecimal. Historically, it is written as MMMCDLX in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 5 × 173) reveals 4 prime building blocks.
Divisible by 2
3460 ends in 0, so it is even.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 60 form a multiple of 4.
Divisible by 5
3460 ends in 0, 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 13 is not a multiple of 9.
Divisible by 10
3460 ends in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 3460 within several notable number theory sequences:
Timeline
Deep dive
How 3460 breaks down
3460 carries 12 distinct factors and a digit signature of 13 (4 as the digital root). The abundant classification indicates that its proper divisors sum to 3848, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110110000100 supports bitwise reasoning, hexadecimal D84 aligns with computing notation, and the Roman numeral MMMCDLX keeps the encyclopedic tradition alive. These attributes make 3460 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3460 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3455–3465) to tune search ranges, and educators feature 3460 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 3460 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 3460
Is 3460 a prime number?
3460 is composite with 12 total factors and the prime factorization 2^2 × 5 × 173.
What is the prime factorization of 3460?
It breaks down as 2^2 × 5 × 173, multiplying the primes 2 × 2 × 5 × 173.
How is 3460 represented in binary and hexadecimal?
3460 converts to 110110000100 in binary and D84 in hexadecimal, which are helpful for computer science applications.
Is 3460 a perfect square, cube, or triangular number?
3460 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3460?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.