3400
3400 is a even composite number that follows 3399 and precedes 3401. It is composed of 24 distinct factors: 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400. Its prime factorization can be written as 2^3 × 5^2 × 17. 3400 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3400 is represented as 110101001000 in binary and D48 in hexadecimal. Historically, it is written as MMMCD in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^3 × 5^2 × 17) reveals 6 prime building blocks.
Divisible by 2
3400 ends in 0, so it is even.
Divisible by 3
The digit sum 7 is not a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
3400 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 7 is not a multiple of 9.
Divisible by 10
3400 ends in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Abundant classification and digit analytics place 3400 within several notable number theory sequences:
Timeline
Deep dive
How 3400 breaks down
3400 carries 24 distinct factors and a digit signature of 7 (7 as the digital root). The abundant classification indicates that its proper divisors sum to 4970, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110101001000 supports bitwise reasoning, hexadecimal D48 aligns with computing notation, and the Roman numeral MMMCD keeps the encyclopedic tradition alive. These attributes make 3400 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3400 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3395–3405) to tune search ranges, and educators feature 3400 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 3400 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 3400
Is 3400 a prime number?
3400 is composite with 24 total factors and the prime factorization 2^3 × 5^2 × 17.
What is the prime factorization of 3400?
It breaks down as 2^3 × 5^2 × 17, multiplying the primes 2 × 2 × 2 × 5 × 5 × 17.
How is 3400 represented in binary and hexadecimal?
3400 converts to 110101001000 in binary and D48 in hexadecimal, which are helpful for computer science applications.
Is 3400 a perfect square, cube, or triangular number?
3400 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3400?
The digits sum to 7, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.