1392
1392 is a even composite number that follows 1391 and precedes 1393. It is composed of 20 distinct factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 29, 48, 58, 87, 116, 174, 232, 348, 464, 696, 1392. Its prime factorization can be written as 2^4 × 3 × 29. 1392 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1392 is represented as 10101110000 in binary and 570 in hexadecimal. Historically, it is written as MCCCXCII in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 3 × 29) reveals 6 prime building blocks.
Divisible by 2
1392 ends in 2, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 92 form a multiple of 4.
Divisible by 5
1392 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
1392 does not end in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 1392 within several notable number theory sequences:
Timeline
Deep dive
How 1392 breaks down
1392 carries 20 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 2328, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10101110000 supports bitwise reasoning, hexadecimal 570 aligns with computing notation, and the Roman numeral MCCCXCII keeps the encyclopedic tradition alive. These attributes make 1392 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1392 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1387–1397) to tune search ranges, and educators feature 1392 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 1392 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 1392
Is 1392 a prime number?
1392 is composite with 20 total factors and the prime factorization 2^4 × 3 × 29.
What is the prime factorization of 1392?
It breaks down as 2^4 × 3 × 29, multiplying the primes 2 × 2 × 2 × 2 × 3 × 29.
How is 1392 represented in binary and hexadecimal?
1392 converts to 10101110000 in binary and 570 in hexadecimal, which are helpful for computer science applications.
Is 1392 a perfect square, cube, or triangular number?
1392 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1392?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.