3407
3407 is a odd prime number that follows 3406 and precedes 3408. As a prime number, 3407 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 3407. 3407 is classified as a deficient number based on the sum of its proper divisors. In computer science, 3407 is represented as 110101001111 in binary and D4F in hexadecimal. Historically, it is written as MMMCDVII in Roman numerals.
Factor Analysis
2 FactorsProperties
3407 is prime, so its only factors are 1 and 3407.
Divisible by 2
3407 ends in 7, so it is odd.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 07 are not divisible by 4.
Divisible by 5
3407 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 14 is not a multiple of 9.
Divisible by 10
3407 does not end in 0.
Divisible by 11
The alternating digit sum -8 is not a multiple of 11.
Deficient classification and digit analytics place 3407 within several notable number theory sequences:
Timeline
Deep dive
How 3407 breaks down
3407 carries 2 distinct factors and a digit signature of 14 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 1, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110101001111 supports bitwise reasoning, hexadecimal D4F aligns with computing notation, and the Roman numeral MMMCDVII keeps the encyclopedic tradition alive. These attributes make 3407 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3407 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3402–3412) to tune search ranges, and educators feature 3407 in worksheets about prime identification. 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 (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 3407 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 3407
Is 3407 a prime number?
3407 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 3407?
3407 is already prime, so the factorization is simply 3407.
How is 3407 represented in binary and hexadecimal?
3407 converts to 110101001111 in binary and D4F in hexadecimal, which are helpful for computer science applications.
Is 3407 a perfect square, cube, or triangular number?
3407 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3407?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.