1701
1701 is a odd composite number that follows 1700 and precedes 1702. It is composed of 12 distinct factors: 1, 3, 7, 9, 21, 27, 63, 81, 189, 243, 567, 1701. Its prime factorization can be written as 3^5 × 7. 1701 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1701 is represented as 11010100101 in binary and 6A5 in hexadecimal. Historically, it is written as MDCCI in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (3^5 × 7) reveals 6 prime building blocks.
Divisible by 2
1701 ends in 1, so it is odd.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 01 are not divisible by 4.
Divisible by 5
1701 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 9 is a multiple of 9.
Divisible by 10
1701 does not end in 0.
Divisible by 11
The alternating digit sum -7 is not a multiple of 11.
Deficient classification and digit analytics place 1701 within several notable number theory sequences:
Timeline
Deep dive
How 1701 breaks down
1701 carries 12 distinct factors and a digit signature of 9 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 1211, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11010100101 supports bitwise reasoning, hexadecimal 6A5 aligns with computing notation, and the Roman numeral MDCCI keeps the encyclopedic tradition alive. These attributes make 1701 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1701 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1696–1706) to tune search ranges, and educators feature 1701 in worksheets about factor trees. Its binary footprint of length 11 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 1701 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 1701
Is 1701 a prime number?
1701 is composite with 12 total factors and the prime factorization 3^5 × 7.
What is the prime factorization of 1701?
It breaks down as 3^5 × 7, multiplying the primes 3 × 3 × 3 × 3 × 3 × 7.
How is 1701 represented in binary and hexadecimal?
1701 converts to 11010100101 in binary and 6A5 in hexadecimal, which are helpful for computer science applications.
Is 1701 a perfect square, cube, or triangular number?
1701 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1701?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.