432
432 is a even composite number that follows 431 and precedes 433. It is composed of 20 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432. Its prime factorization can be written as 2^4 × 3^3. 432 is classified as a abundant number based on the sum of its proper divisors. In computer science, 432 is represented as 110110000 in binary and 1B0 in hexadecimal. Historically, it is written as CDXXXII in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 3^3) reveals 7 prime building blocks.
Divisible by 2
432 ends in 2, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 32 form a multiple of 4.
Divisible by 5
432 does not end in 0 or 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 9 is a multiple of 9.
Divisible by 10
432 does not end in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Abundant classification and digit analytics place 432 within several notable number theory sequences:
Timeline
Deep dive
How 432 breaks down
432 carries 20 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 808, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110110000 supports bitwise reasoning, hexadecimal 1B0 aligns with computing notation, and the Roman numeral CDXXXII keeps the encyclopedic tradition alive. These attributes make 432 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 432 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (427–437) to tune search ranges, and educators feature 432 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 432 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 432
Is 432 a prime number?
432 is composite with 20 total factors and the prime factorization 2^4 × 3^3.
What is the prime factorization of 432?
It breaks down as 2^4 × 3^3, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3 × 3.
How is 432 represented in binary and hexadecimal?
432 converts to 110110000 in binary and 1B0 in hexadecimal, which are helpful for computer science applications.
Is 432 a perfect square, cube, or triangular number?
432 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 432?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.