5460
5460 is a even composite number that follows 5459 and precedes 5461. It is composed of 48 distinct factors: 1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28, 30, 35, 39, 42, 52, 60, 65, 70, 78, 84, 91, 105, 130, 140, 156, 182, 195, 210, 260, 273, 364, 390, 420, 455, 546, 780, 910, 1092, 1365, 1820, 2730, 5460. Its prime factorization can be written as 2^2 × 3 × 5 × 7 × 13. 5460 is classified as a abundant number based on the sum of its proper divisors. In computer science, 5460 is represented as 1010101010100 in binary and 1554 in hexadecimal. It also belongs to the triangular number sequence.
Factor Analysis
48 FactorsProperties
The prime factorization (2^2 × 3 × 5 × 7 × 13) reveals 6 prime building blocks.
Divisible by 2
5460 ends in 0, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 60 form a multiple of 4.
Divisible by 5
5460 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 15 is not a multiple of 9.
Divisible by 10
5460 ends in 0.
Divisible by 11
The alternating digit sum 7 is not a multiple of 11.
Abundant classification and digit analytics place 5460 within several notable number theory sequences:
Timeline
Deep dive
How 5460 breaks down
5460 carries 48 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 13356, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1010101010100 supports bitwise reasoning, hexadecimal 1554 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 5460 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 5460 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (5455–5465) to tune search ranges, and educators feature 5460 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, Triangular numbers) help historians, numerologists, and trivia writers tie 5460 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 5460
Is 5460 a prime number?
5460 is composite with 48 total factors and the prime factorization 2^2 × 3 × 5 × 7 × 13.
What is the prime factorization of 5460?
It breaks down as 2^2 × 3 × 5 × 7 × 13, multiplying the primes 2 × 2 × 3 × 5 × 7 × 13.
How is 5460 represented in binary and hexadecimal?
5460 converts to 1010101010100 in binary and 1554 in hexadecimal, which are helpful for computer science applications.
Is 5460 a perfect square, cube, or triangular number?
5460 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 5460?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.