1464
1464 is a even composite number that follows 1463 and precedes 1465. It is composed of 16 distinct factors: 1, 2, 3, 4, 6, 8, 12, 24, 61, 122, 183, 244, 366, 488, 732, 1464. Its prime factorization can be written as 2^3 × 3 × 61. 1464 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1464 is represented as 10110111000 in binary and 5B8 in hexadecimal. Historically, it is written as MCDLXIV in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2^3 × 3 × 61) reveals 5 prime building blocks.
Divisible by 2
1464 ends in 4, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
1464 does not end in 0 or 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
1464 does not end in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Abundant classification and digit analytics place 1464 within several notable number theory sequences:
Timeline
Deep dive
How 1464 breaks down
1464 carries 16 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 2256, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10110111000 supports bitwise reasoning, hexadecimal 5B8 aligns with computing notation, and the Roman numeral MCDLXIV keeps the encyclopedic tradition alive. These attributes make 1464 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1464 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1459–1469) to tune search ranges, and educators feature 1464 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 1464 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 1464
Is 1464 a prime number?
1464 is composite with 16 total factors and the prime factorization 2^3 × 3 × 61.
What is the prime factorization of 1464?
It breaks down as 2^3 × 3 × 61, multiplying the primes 2 × 2 × 2 × 3 × 61.
How is 1464 represented in binary and hexadecimal?
1464 converts to 10110111000 in binary and 5B8 in hexadecimal, which are helpful for computer science applications.
Is 1464 a perfect square, cube, or triangular number?
1464 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1464?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.