13400
13400 is a even composite number that follows 13399 and precedes 13401. It is composed of 24 distinct factors: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 67, 100, 134, 200, 268, 335, 536, 670, 1340, 1675, 2680, 3350, 6700, 13400. Its prime factorization can be written as 2^3 × 5^2 × 67. 13400 is classified as a abundant number based on the sum of its proper divisors. In computer science, 13400 is represented as 11010001011000 in binary and 3458 in hexadecimal.
Factor Analysis
24 FactorsProperties
The prime factorization (2^3 × 5^2 × 67) reveals 6 prime building blocks.
Divisible by 2
13400 ends in 0, so it is even.
Divisible by 3
The digit sum 8 is not a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
13400 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 8 is not a multiple of 9.
Divisible by 10
13400 ends in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 13400 within several notable number theory sequences:
Timeline
Deep dive
How 13400 breaks down
13400 carries 24 distinct factors and a digit signature of 8 (8 as the digital root). The abundant classification indicates that its proper divisors sum to 18220, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11010001011000 supports bitwise reasoning, hexadecimal 3458 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 13400 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 13400 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (13395–13405) to tune search ranges, and educators feature 13400 in worksheets about factor trees. Its binary footprint of length 14 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 13400 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 13400
Is 13400 a prime number?
13400 is composite with 24 total factors and the prime factorization 2^3 × 5^2 × 67.
What is the prime factorization of 13400?
It breaks down as 2^3 × 5^2 × 67, multiplying the primes 2 × 2 × 2 × 5 × 5 × 67.
How is 13400 represented in binary and hexadecimal?
13400 converts to 11010001011000 in binary and 3458 in hexadecimal, which are helpful for computer science applications.
Is 13400 a perfect square, cube, or triangular number?
13400 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 13400?
The digits sum to 8, producing a digital root of 8. These tests power divisibility shortcuts for 3 and 9.