1410
1410 is a even composite number that follows 1409 and precedes 1411. It is composed of 16 distinct factors: 1, 2, 3, 5, 6, 10, 15, 30, 47, 94, 141, 235, 282, 470, 705, 1410. Its prime factorization can be written as 2 × 3 × 5 × 47. 1410 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1410 is represented as 10110000010 in binary and 582 in hexadecimal. Historically, it is written as MCDX in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2 × 3 × 5 × 47) reveals 4 prime building blocks.
Divisible by 2
1410 ends in 0, so it is even.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 10 are not divisible by 4.
Divisible by 5
1410 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 6 is not a multiple of 9.
Divisible by 10
1410 ends in 0.
Divisible by 11
The alternating digit sum -2 is not a multiple of 11.
Abundant classification and digit analytics place 1410 within several notable number theory sequences:
Timeline
Deep dive
How 1410 breaks down
1410 carries 16 distinct factors and a digit signature of 6 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 2046, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10110000010 supports bitwise reasoning, hexadecimal 582 aligns with computing notation, and the Roman numeral MCDX keeps the encyclopedic tradition alive. These attributes make 1410 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1410 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1405–1415) to tune search ranges, and educators feature 1410 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 1410 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 1410
Is 1410 a prime number?
1410 is composite with 16 total factors and the prime factorization 2 × 3 × 5 × 47.
What is the prime factorization of 1410?
It breaks down as 2 × 3 × 5 × 47, multiplying the primes 2 × 3 × 5 × 47.
How is 1410 represented in binary and hexadecimal?
1410 converts to 10110000010 in binary and 582 in hexadecimal, which are helpful for computer science applications.
Is 1410 a perfect square, cube, or triangular number?
1410 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1410?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.