31200
31200 is a even composite number that follows 31199 and precedes 31201. It is composed of 72 distinct factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26, 30, 32, 39, 40, 48, 50, 52, 60, 65, 75, 78, 80, 96, 100, 104, 120, 130, 150, 156, 160, 195, 200, 208, 240, 260, 300, 312, 325, 390, 400, 416, 480, 520, 600, 624, 650, 780, 800, 975, 1040, 1200, 1248, 1300, 1560, 1950, 2080, 2400, 2600, 3120, 3900, 5200, 6240, 7800, 10400, 15600, 31200. Its prime factorization can be written as 2^5 × 3 × 5^2 × 13. 31200 is classified as a abundant number based on the sum of its proper divisors. In computer science, 31200 is represented as 111100111100000 in binary and 79E0 in hexadecimal.
Factor Analysis
72 FactorsProperties
The prime factorization (2^5 × 3 × 5^2 × 13) reveals 9 prime building blocks.
Divisible by 2
31200 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 00 form a multiple of 4.
Divisible by 5
31200 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
31200 ends in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Abundant classification and digit analytics place 31200 within several notable number theory sequences:
Timeline
Deep dive
How 31200 breaks down
31200 carries 72 distinct factors and a digit signature of 6 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 78168, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111100111100000 supports bitwise reasoning, hexadecimal 79E0 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 31200 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 31200 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (31195–31205) to tune search ranges, and educators feature 31200 in worksheets about factor trees. Its binary footprint of length 15 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 31200 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 31200
Is 31200 a prime number?
31200 is composite with 72 total factors and the prime factorization 2^5 × 3 × 5^2 × 13.
What is the prime factorization of 31200?
It breaks down as 2^5 × 3 × 5^2 × 13, multiplying the primes 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5 × 13.
How is 31200 represented in binary and hexadecimal?
31200 converts to 111100111100000 in binary and 79E0 in hexadecimal, which are helpful for computer science applications.
Is 31200 a perfect square, cube, or triangular number?
31200 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 31200?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.