2401
2401 is a odd composite number that follows 2400 and precedes 2402. It is composed of 5 distinct factors: 1, 7, 49, 343, 2401. Its prime factorization can be written as 7^4. 2401 is classified as a deficient number based on the sum of its proper divisors. In computer science, 2401 is represented as 100101100001 in binary and 961 in hexadecimal. Historically, it is written as MMCDI in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
5 FactorsProperties
The prime factorization (7^4) reveals 4 prime building blocks.
Divisible by 2
2401 ends in 1, so it is odd.
Divisible by 3
The digit sum 7 is not a multiple of 3.
Divisible by 4
The last two digits 01 are not divisible by 4.
Divisible by 5
2401 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 7 is not a multiple of 9.
Divisible by 10
2401 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Deficient classification and digit analytics place 2401 within several notable number theory sequences:
Timeline
Deep dive
How 2401 breaks down
2401 carries 5 distinct factors and a digit signature of 7 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 400, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100101100001 supports bitwise reasoning, hexadecimal 961 aligns with computing notation, and the Roman numeral MMCDI keeps the encyclopedic tradition alive. These attributes make 2401 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2401 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2396–2406) to tune search ranges, and educators feature 2401 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, Deficient numbers, Perfect squares) help historians, numerologists, and trivia writers tie 2401 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 2401
Is 2401 a prime number?
2401 is composite with 5 total factors and the prime factorization 7^4.
What is the prime factorization of 2401?
It breaks down as 7^4, multiplying the primes 7 × 7 × 7 × 7.
How is 2401 represented in binary and hexadecimal?
2401 converts to 100101100001 in binary and 961 in hexadecimal, which are helpful for computer science applications.
Is 2401 a perfect square, cube, or triangular number?
2401 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2401?
The digits sum to 7, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.