3402
3402 is a even composite number that follows 3401 and precedes 3403. It is composed of 24 distinct factors: 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 243, 378, 486, 567, 1134, 1701, 3402. Its prime factorization can be written as 2 × 3^5 × 7. 3402 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3402 is represented as 110101001010 in binary and D4A in hexadecimal. Historically, it is written as MMMCDII in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2 × 3^5 × 7) reveals 7 prime building blocks.
Divisible by 2
3402 ends in 2, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 02 are not divisible by 4.
Divisible by 5
3402 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 9 is a multiple of 9.
Divisible by 10
3402 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 3402 within several notable number theory sequences:
Timeline
Deep dive
How 3402 breaks down
3402 carries 24 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 5334, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110101001010 supports bitwise reasoning, hexadecimal D4A aligns with computing notation, and the Roman numeral MMMCDII keeps the encyclopedic tradition alive. These attributes make 3402 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3402 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3397–3407) to tune search ranges, and educators feature 3402 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 3402 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 3402
Is 3402 a prime number?
3402 is composite with 24 total factors and the prime factorization 2 × 3^5 × 7.
What is the prime factorization of 3402?
It breaks down as 2 × 3^5 × 7, multiplying the primes 2 × 3 × 3 × 3 × 3 × 3 × 7.
How is 3402 represented in binary and hexadecimal?
3402 converts to 110101001010 in binary and D4A in hexadecimal, which are helpful for computer science applications.
Is 3402 a perfect square, cube, or triangular number?
3402 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3402?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.