420
420 is a even composite number that follows 419 and precedes 421. It is composed of 24 distinct factors: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420. Its prime factorization can be written as 2^2 × 3 × 5 × 7. 420 is classified as a abundant number based on the sum of its proper divisors. In computer science, 420 is represented as 110100100 in binary and 1A4 in hexadecimal. Historically, it is written as CDXX in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^2 × 3 × 5 × 7) reveals 5 prime building blocks.
Divisible by 2
420 ends in 0, so it is even.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 20 form a multiple of 4.
Divisible by 5
420 ends in 0, so it is divisible by 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 6 is not a multiple of 9.
Divisible by 10
420 ends in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 420 within several notable number theory sequences:
Timeline
Deep dive
How 420 breaks down
420 carries 24 distinct factors and a digit signature of 6 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 924, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110100100 supports bitwise reasoning, hexadecimal 1A4 aligns with computing notation, and the Roman numeral CDXX keeps the encyclopedic tradition alive. These attributes make 420 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 420 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (415–425) to tune search ranges, and educators feature 420 in worksheets about factor trees. 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 (Composite numbers, Abundant numbers) help historians, numerologists, and trivia writers tie 420 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 420
Is 420 a prime number?
420 is composite with 24 total factors and the prime factorization 2^2 × 3 × 5 × 7.
What is the prime factorization of 420?
It breaks down as 2^2 × 3 × 5 × 7, multiplying the primes 2 × 2 × 3 × 5 × 7.
How is 420 represented in binary and hexadecimal?
420 converts to 110100100 in binary and 1A4 in hexadecimal, which are helpful for computer science applications.
Is 420 a perfect square, cube, or triangular number?
420 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 420?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.