1026
1026 is a even composite number that follows 1025 and precedes 1027. It is composed of 16 distinct factors: 1, 2, 3, 6, 9, 18, 19, 27, 38, 54, 57, 114, 171, 342, 513, 1026. Its prime factorization can be written as 2 × 3^3 × 19. 1026 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1026 is represented as 10000000010 in binary and 402 in hexadecimal. Historically, it is written as MXXVI in Roman numerals.
Factor Analysis
16 FactorsProperties
The prime factorization (2 × 3^3 × 19) reveals 5 prime building blocks.
Divisible by 2
1026 ends in 6, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 26 are not divisible by 4.
Divisible by 5
1026 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 9 is a multiple of 9.
Divisible by 10
1026 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 1026 within several notable number theory sequences:
Timeline
Deep dive
How 1026 breaks down
1026 carries 16 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 1374, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000000010 supports bitwise reasoning, hexadecimal 402 aligns with computing notation, and the Roman numeral MXXVI keeps the encyclopedic tradition alive. These attributes make 1026 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1026 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1021–1031) to tune search ranges, and educators feature 1026 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 1026 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 1026
Is 1026 a prime number?
1026 is composite with 16 total factors and the prime factorization 2 × 3^3 × 19.
What is the prime factorization of 1026?
It breaks down as 2 × 3^3 × 19, multiplying the primes 2 × 3 × 3 × 3 × 19.
How is 1026 represented in binary and hexadecimal?
1026 converts to 10000000010 in binary and 402 in hexadecimal, which are helpful for computer science applications.
Is 1026 a perfect square, cube, or triangular number?
1026 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1026?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.