400
400 is a even composite number that follows 399 and precedes 401. It is composed of 15 distinct factors: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400. Its prime factorization can be written as 2^4 × 5^2. 400 is classified as a abundant number based on the sum of its proper divisors. In computer science, 400 is represented as 110010000 in binary and 190 in hexadecimal. Historically, it is written as CD in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
15 FactorsProperties
The prime factorization (2^4 × 5^2) reveals 6 prime building blocks.
Divisible by 2
400 ends in 0, so it is even.
Divisible by 3
The digit sum 4 is not a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
400 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 4 is not a multiple of 9.
Divisible by 10
400 ends in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Abundant classification and digit analytics place 400 within several notable number theory sequences:
Timeline
Deep dive
How 400 breaks down
400 carries 15 distinct factors and a digit signature of 4 (4 as the digital root). The abundant classification indicates that its proper divisors sum to 561, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110010000 supports bitwise reasoning, hexadecimal 190 aligns with computing notation, and the Roman numeral CD keeps the encyclopedic tradition alive. These attributes make 400 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 400 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (395–405) to tune search ranges, and educators feature 400 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, Perfect squares) help historians, numerologists, and trivia writers tie 400 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 400
Is 400 a prime number?
400 is composite with 15 total factors and the prime factorization 2^4 × 5^2.
What is the prime factorization of 400?
It breaks down as 2^4 × 5^2, multiplying the primes 2 × 2 × 2 × 2 × 5 × 5.
How is 400 represented in binary and hexadecimal?
400 converts to 110010000 in binary and 190 in hexadecimal, which are helpful for computer science applications.
Is 400 a perfect square, cube, or triangular number?
400 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 400?
The digits sum to 4, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.