1260
1260 is a even composite number that follows 1259 and precedes 1261. It is composed of 36 distinct factors: 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260. Its prime factorization can be written as 2^2 × 3^2 × 5 × 7. 1260 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1260 is represented as 10011101100 in binary and 4EC in hexadecimal. Historically, it is written as MCCLX in Roman numerals.
Factor Analysis
36 FactorsProperties
The prime factorization (2^2 × 3^2 × 5 × 7) reveals 6 prime building blocks.
Divisible by 2
1260 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 60 form a multiple of 4.
Divisible by 5
1260 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
1260 ends in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 1260 within several notable number theory sequences:
Timeline
Deep dive
How 1260 breaks down
1260 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 3108, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10011101100 supports bitwise reasoning, hexadecimal 4EC aligns with computing notation, and the Roman numeral MCCLX keeps the encyclopedic tradition alive. These attributes make 1260 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1260 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1255–1265) to tune search ranges, and educators feature 1260 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 1260 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 1260
Is 1260 a prime number?
1260 is composite with 36 total factors and the prime factorization 2^2 × 3^2 × 5 × 7.
What is the prime factorization of 1260?
It breaks down as 2^2 × 3^2 × 5 × 7, multiplying the primes 2 × 2 × 3 × 3 × 5 × 7.
How is 1260 represented in binary and hexadecimal?
1260 converts to 10011101100 in binary and 4EC in hexadecimal, which are helpful for computer science applications.
Is 1260 a perfect square, cube, or triangular number?
1260 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1260?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.