421
421 is a odd prime number that follows 420 and precedes 422. As a prime number, 421 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 421. 421 is classified as a deficient number based on the sum of its proper divisors. In computer science, 421 is represented as 110100101 in binary and 1A5 in hexadecimal. Historically, it is written as CDXXI in Roman numerals.
Factor Analysis
2 FactorsProperties
421 is prime, so its only factors are 1 and 421.
Divisible by 2
421 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 21 are not divisible by 4.
Divisible by 5
421 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
421 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 421 within several notable number theory sequences:
Timeline
Deep dive
How 421 breaks down
421 carries 2 distinct factors and a digit signature of 7 (7 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 110100101 supports bitwise reasoning, hexadecimal 1A5 aligns with computing notation, and the Roman numeral CDXXI keeps the encyclopedic tradition alive. These attributes make 421 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 421 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (416–426) to tune search ranges, and educators feature 421 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 421 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 421
Is 421 a prime number?
421 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 421?
421 is already prime, so the factorization is simply 421.
How is 421 represented in binary and hexadecimal?
421 converts to 110100101 in binary and 1A5 in hexadecimal, which are helpful for computer science applications.
Is 421 a perfect square, cube, or triangular number?
421 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 421?
The digits sum to 7, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.