77013
77013 is a odd composite number that follows 77012 and precedes 77014. It is composed of 12 distinct factors: 1, 3, 9, 43, 129, 199, 387, 597, 1791, 8557, 25671, 77013. Its prime factorization can be written as 3^2 × 43 × 199. 77013 is classified as a deficient number based on the sum of its proper divisors. In computer science, 77013 is represented as 10010110011010101 in binary and 12CD5 in hexadecimal.
Factor Analysis
12 FactorsProperties
The prime factorization (3^2 × 43 × 199) reveals 4 prime building blocks.
Divisible by 2
77013 ends in 3, so it is odd.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 13 are not divisible by 4.
Divisible by 5
77013 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 18 is a multiple of 9.
Divisible by 10
77013 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Deficient classification and digit analytics place 77013 within several notable number theory sequences:
Timeline
Deep dive
How 77013 breaks down
77013 carries 12 distinct factors and a digit signature of 18 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 37387, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10010110011010101 supports bitwise reasoning, hexadecimal 12CD5 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 77013 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 77013 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (77008–77018) to tune search ranges, and educators feature 77013 in worksheets about factor trees. Its binary footprint of length 17 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 77013 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 77013
Is 77013 a prime number?
77013 is composite with 12 total factors and the prime factorization 3^2 × 43 × 199.
What is the prime factorization of 77013?
It breaks down as 3^2 × 43 × 199, multiplying the primes 3 × 3 × 43 × 199.
How is 77013 represented in binary and hexadecimal?
77013 converts to 10010110011010101 in binary and 12CD5 in hexadecimal, which are helpful for computer science applications.
Is 77013 a perfect square, cube, or triangular number?
77013 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 77013?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.