5880
5880 is a even composite number that follows 5879 and precedes 5881. It is composed of 48 distinct factors: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 49, 56, 60, 70, 84, 98, 105, 120, 140, 147, 168, 196, 210, 245, 280, 294, 392, 420, 490, 588, 735, 840, 980, 1176, 1470, 1960, 2940, 5880. Its prime factorization can be written as 2^3 × 3 × 5 × 7^2. 5880 is classified as a abundant number based on the sum of its proper divisors. In computer science, 5880 is represented as 1011011111000 in binary and 16F8 in hexadecimal.
Factor Analysis
48 FactorsProperties
The prime factorization (2^3 × 3 × 5 × 7^2) reveals 7 prime building blocks.
Divisible by 2
5880 ends in 0, so it is even.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
5880 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 21 is not a multiple of 9.
Divisible by 10
5880 ends in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 5880 within several notable number theory sequences:
Timeline
Deep dive
How 5880 breaks down
5880 carries 48 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 14640, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1011011111000 supports bitwise reasoning, hexadecimal 16F8 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 5880 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 5880 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (5875–5885) to tune search ranges, and educators feature 5880 in worksheets about factor trees. Its binary footprint of length 13 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 5880 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 5880
Is 5880 a prime number?
5880 is composite with 48 total factors and the prime factorization 2^3 × 3 × 5 × 7^2.
What is the prime factorization of 5880?
It breaks down as 2^3 × 3 × 5 × 7^2, multiplying the primes 2 × 2 × 2 × 3 × 5 × 7 × 7.
How is 5880 represented in binary and hexadecimal?
5880 converts to 1011011111000 in binary and 16F8 in hexadecimal, which are helpful for computer science applications.
Is 5880 a perfect square, cube, or triangular number?
5880 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 5880?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.