1022
1022 is a even composite number that follows 1021 and precedes 1023. It is composed of 8 distinct factors: 1, 2, 7, 14, 73, 146, 511, 1022. Its prime factorization can be written as 2 × 7 × 73. 1022 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1022 is represented as 1111111110 in binary and 3FE in hexadecimal. Historically, it is written as MXXII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 7 × 73) reveals 3 prime building blocks.
Divisible by 2
1022 ends in 2, so it is even.
Divisible by 3
The digit sum 5 is not a multiple of 3.
Divisible by 4
The last two digits 22 are not divisible by 4.
Divisible by 5
1022 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 5 is not a multiple of 9.
Divisible by 10
1022 does not end in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Deficient classification and digit analytics place 1022 within several notable number theory sequences:
Timeline
Deep dive
How 1022 breaks down
1022 carries 8 distinct factors and a digit signature of 5 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 754, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111111110 supports bitwise reasoning, hexadecimal 3FE aligns with computing notation, and the Roman numeral MXXII keeps the encyclopedic tradition alive. These attributes make 1022 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1022 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1017–1027) to tune search ranges, and educators feature 1022 in worksheets about factor trees. Its binary footprint of length 10 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 1022 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 1022
Is 1022 a prime number?
1022 is composite with 8 total factors and the prime factorization 2 × 7 × 73.
What is the prime factorization of 1022?
It breaks down as 2 × 7 × 73, multiplying the primes 2 × 7 × 73.
How is 1022 represented in binary and hexadecimal?
1022 converts to 1111111110 in binary and 3FE in hexadecimal, which are helpful for computer science applications.
Is 1022 a perfect square, cube, or triangular number?
1022 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1022?
The digits sum to 5, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.