42480
42480 is a even composite number that follows 42479 and precedes 42481. It is composed of 60 distinct factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 59, 60, 72, 80, 90, 118, 120, 144, 177, 180, 236, 240, 295, 354, 360, 472, 531, 590, 708, 720, 885, 944, 1062, 1180, 1416, 1770, 2124, 2360, 2655, 2832, 3540, 4248, 4720, 5310, 7080, 8496, 10620, 14160, 21240, 42480. Its prime factorization can be written as 2^4 × 3^2 × 5 × 59. 42480 is classified as a abundant number based on the sum of its proper divisors. In computer science, 42480 is represented as 1010010111110000 in binary and A5F0 in hexadecimal.
Factor Analysis
60 FactorsProperties
The prime factorization (2^4 × 3^2 × 5 × 59) reveals 8 prime building blocks.
Divisible by 2
42480 ends in 0, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
42480 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 18 is a multiple of 9.
Divisible by 10
42480 ends in 0.
Divisible by 11
The alternating digit sum -2 is not a multiple of 11.
Abundant classification and digit analytics place 42480 within several notable number theory sequences:
Timeline
Deep dive
How 42480 breaks down
42480 carries 60 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 102600, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010010111110000 supports bitwise reasoning, hexadecimal A5F0 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 42480 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 42480 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (42475–42485) to tune search ranges, and educators feature 42480 in worksheets about factor trees. Its binary footprint of length 16 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 42480 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 42480
Is 42480 a prime number?
42480 is composite with 60 total factors and the prime factorization 2^4 × 3^2 × 5 × 59.
What is the prime factorization of 42480?
It breaks down as 2^4 × 3^2 × 5 × 59, multiplying the primes 2 × 2 × 2 × 2 × 3 × 3 × 5 × 59.
How is 42480 represented in binary and hexadecimal?
42480 converts to 1010010111110000 in binary and A5F0 in hexadecimal, which are helpful for computer science applications.
Is 42480 a perfect square, cube, or triangular number?
42480 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 42480?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.