1456
1456 is a even composite number that follows 1455 and precedes 1457. It is composed of 20 distinct factors: 1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 52, 56, 91, 104, 112, 182, 208, 364, 728, 1456. Its prime factorization can be written as 2^4 × 7 × 13. 1456 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1456 is represented as 10110110000 in binary and 5B0 in hexadecimal. Historically, it is written as MCDLVI in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 7 × 13) reveals 6 prime building blocks.
Divisible by 2
1456 ends in 6, so it is even.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 56 form a multiple of 4.
Divisible by 5
1456 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 16 is not a multiple of 9.
Divisible by 10
1456 does not end in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Abundant classification and digit analytics place 1456 within several notable number theory sequences:
Timeline
Deep dive
How 1456 breaks down
1456 carries 20 distinct factors and a digit signature of 16 (7 as the digital root). The abundant classification indicates that its proper divisors sum to 2016, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10110110000 supports bitwise reasoning, hexadecimal 5B0 aligns with computing notation, and the Roman numeral MCDLVI keeps the encyclopedic tradition alive. These attributes make 1456 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1456 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1451–1461) to tune search ranges, and educators feature 1456 in worksheets about factor trees. Its binary footprint of length 11 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 1456 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 1456
Is 1456 a prime number?
1456 is composite with 20 total factors and the prime factorization 2^4 × 7 × 13.
What is the prime factorization of 1456?
It breaks down as 2^4 × 7 × 13, multiplying the primes 2 × 2 × 2 × 2 × 7 × 13.
How is 1456 represented in binary and hexadecimal?
1456 converts to 10110110000 in binary and 5B0 in hexadecimal, which are helpful for computer science applications.
Is 1456 a perfect square, cube, or triangular number?
1456 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1456?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.