1013
1013 is a odd prime number that follows 1012 and precedes 1014. As a prime number, 1013 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 1013. 1013 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1013 is represented as 1111110101 in binary and 3F5 in hexadecimal. Historically, it is written as MXIII in Roman numerals.
Factor Analysis
2 FactorsProperties
1013 is prime, so its only factors are 1 and 1013.
Divisible by 2
1013 ends in 3, so it is odd.
Divisible by 3
The digit sum 5 is not a multiple of 3.
Divisible by 4
The last two digits 13 are not divisible by 4.
Divisible by 5
1013 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
1013 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 1013 within several notable number theory sequences:
Timeline
Deep dive
How 1013 breaks down
1013 carries 2 distinct factors and a digit signature of 5 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 1, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111110101 supports bitwise reasoning, hexadecimal 3F5 aligns with computing notation, and the Roman numeral MXIII keeps the encyclopedic tradition alive. These attributes make 1013 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1013 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1008–1018) to tune search ranges, and educators feature 1013 in worksheets about prime identification. 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 (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 1013 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 1013
Is 1013 a prime number?
1013 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 1013?
1013 is already prime, so the factorization is simply 1013.
How is 1013 represented in binary and hexadecimal?
1013 converts to 1111110101 in binary and 3F5 in hexadecimal, which are helpful for computer science applications.
Is 1013 a perfect square, cube, or triangular number?
1013 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1013?
The digits sum to 5, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.