1440
1440 is a even composite number that follows 1439 and precedes 1441. It is composed of 36 distinct factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 360, 480, 720, 1440. Its prime factorization can be written as 2^5 × 3^2 × 5. 1440 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1440 is represented as 10110100000 in binary and 5A0 in hexadecimal. Historically, it is written as MCDXL in Roman numerals.
Factor Analysis
36 FactorsProperties
The prime factorization (2^5 × 3^2 × 5) reveals 8 prime building blocks.
Divisible by 2
1440 ends in 0, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
1440 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 9 is a multiple of 9.
Divisible by 10
1440 ends in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Abundant classification and digit analytics place 1440 within several notable number theory sequences:
Timeline
Deep dive
How 1440 breaks down
1440 carries 36 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 3474, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10110100000 supports bitwise reasoning, hexadecimal 5A0 aligns with computing notation, and the Roman numeral MCDXL keeps the encyclopedic tradition alive. These attributes make 1440 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1440 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1435–1445) to tune search ranges, and educators feature 1440 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 1440 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 1440
Is 1440 a prime number?
1440 is composite with 36 total factors and the prime factorization 2^5 × 3^2 × 5.
What is the prime factorization of 1440?
It breaks down as 2^5 × 3^2 × 5, multiplying the primes 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5.
How is 1440 represented in binary and hexadecimal?
1440 converts to 10110100000 in binary and 5A0 in hexadecimal, which are helpful for computer science applications.
Is 1440 a perfect square, cube, or triangular number?
1440 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1440?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.