401
401 is a odd prime number that follows 400 and precedes 402. As a prime number, 401 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 401. 401 is classified as a deficient number based on the sum of its proper divisors. In computer science, 401 is represented as 110010001 in binary and 191 in hexadecimal. Historically, it is written as CDI in Roman numerals.
Factor Analysis
2 FactorsProperties
401 is prime, so its only factors are 1 and 401.
Divisible by 2
401 ends in 1, so it is odd.
Divisible by 3
The digit sum 5 is not a multiple of 3.
Divisible by 4
The last two digits 01 are not divisible by 4.
Divisible by 5
401 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 5 is not a multiple of 9.
Divisible by 10
401 does not end in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Deficient classification and digit analytics place 401 within several notable number theory sequences:
Timeline
Deep dive
How 401 breaks down
401 carries 2 distinct factors and a digit signature of 5 (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 110010001 supports bitwise reasoning, hexadecimal 191 aligns with computing notation, and the Roman numeral CDI keeps the encyclopedic tradition alive. These attributes make 401 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 401 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (396–406) to tune search ranges, and educators feature 401 in worksheets about prime identification. Its binary footprint of length 9 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 401 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 401
Is 401 a prime number?
401 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 401?
401 is already prime, so the factorization is simply 401.
How is 401 represented in binary and hexadecimal?
401 converts to 110010001 in binary and 191 in hexadecimal, which are helpful for computer science applications.
Is 401 a perfect square, cube, or triangular number?
401 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 401?
The digits sum to 5, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.