7480
7480 is a even composite number that follows 7479 and precedes 7481. It is composed of 32 distinct factors: 1, 2, 4, 5, 8, 10, 11, 17, 20, 22, 34, 40, 44, 55, 68, 85, 88, 110, 136, 170, 187, 220, 340, 374, 440, 680, 748, 935, 1496, 1870, 3740, 7480. Its prime factorization can be written as 2^3 × 5 × 11 × 17. 7480 is classified as a abundant number based on the sum of its proper divisors. In computer science, 7480 is represented as 1110100111000 in binary and 1D38 in hexadecimal.
Factor Analysis
32 FactorsProperties
The prime factorization (2^3 × 5 × 11 × 17) reveals 6 prime building blocks.
Divisible by 2
7480 ends in 0, so it is even.
Divisible by 3
The digit sum 19 is not a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
7480 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 19 is not a multiple of 9.
Divisible by 10
7480 ends in 0.
Divisible by 11
The alternating digit sum 11 is a multiple of 11.
Abundant classification and digit analytics place 7480 within several notable number theory sequences:
Timeline
Deep dive
How 7480 breaks down
7480 carries 32 distinct factors and a digit signature of 19 (1 as the digital root). The abundant classification indicates that its proper divisors sum to 11960, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1110100111000 supports bitwise reasoning, hexadecimal 1D38 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7480 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7480 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7475–7485) to tune search ranges, and educators feature 7480 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 7480 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 7480
Is 7480 a prime number?
7480 is composite with 32 total factors and the prime factorization 2^3 × 5 × 11 × 17.
What is the prime factorization of 7480?
It breaks down as 2^3 × 5 × 11 × 17, multiplying the primes 2 × 2 × 2 × 5 × 11 × 17.
How is 7480 represented in binary and hexadecimal?
7480 converts to 1110100111000 in binary and 1D38 in hexadecimal, which are helpful for computer science applications.
Is 7480 a perfect square, cube, or triangular number?
7480 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 7480?
The digits sum to 19, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.