1428
1428 is a even composite number that follows 1427 and precedes 1429. It is composed of 24 distinct factors: 1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 68, 84, 102, 119, 204, 238, 357, 476, 714, 1428. Its prime factorization can be written as 2^2 × 3 × 7 × 17. 1428 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1428 is represented as 10110010100 in binary and 594 in hexadecimal. Historically, it is written as MCDXXVIII in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^2 × 3 × 7 × 17) reveals 5 prime building blocks.
Divisible by 2
1428 ends in 8, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 28 form a multiple of 4.
Divisible by 5
1428 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 15 is not a multiple of 9.
Divisible by 10
1428 does not end in 0.
Divisible by 11
The alternating digit sum -9 is not a multiple of 11.
Abundant classification and digit analytics place 1428 within several notable number theory sequences:
Timeline
Deep dive
How 1428 breaks down
1428 carries 24 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 2604, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10110010100 supports bitwise reasoning, hexadecimal 594 aligns with computing notation, and the Roman numeral MCDXXVIII keeps the encyclopedic tradition alive. These attributes make 1428 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1428 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1423–1433) to tune search ranges, and educators feature 1428 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 1428 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 1428
Is 1428 a prime number?
1428 is composite with 24 total factors and the prime factorization 2^2 × 3 × 7 × 17.
What is the prime factorization of 1428?
It breaks down as 2^2 × 3 × 7 × 17, multiplying the primes 2 × 2 × 3 × 7 × 17.
How is 1428 represented in binary and hexadecimal?
1428 converts to 10110010100 in binary and 594 in hexadecimal, which are helpful for computer science applications.
Is 1428 a perfect square, cube, or triangular number?
1428 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1428?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.