61
61 is a odd prime number that follows 60 and precedes 62. As a prime number, 61 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 61. 61 is classified as a deficient number based on the sum of its proper divisors. In computer science, 61 is represented as 111101 in binary and 3D in hexadecimal. Historically, it is written as LXI in Roman numerals.
Factor Analysis
2 FactorsProperties
61 is prime, so its only factors are 1 and 61.
Divisible by 2
61 ends in 1, so it is odd.
Divisible by 3
The digit sum 7 is not a multiple of 3.
Divisible by 4
The last two digits 61 are not divisible by 4.
Divisible by 5
61 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 7 is not a multiple of 9.
Divisible by 10
61 does not end in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Deficient classification and digit analytics place 61 within several notable number theory sequences:
Timeline
Deep dive
How 61 breaks down
61 carries 2 distinct factors and a digit signature of 7 (7 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 111101 supports bitwise reasoning, hexadecimal 3D aligns with computing notation, and the Roman numeral LXI keeps the encyclopedic tradition alive. These attributes make 61 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 61 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (56–66) to tune search ranges, and educators feature 61 in worksheets about prime identification. Its binary footprint of length 6 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 61 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 61
Is 61 a prime number?
61 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 61?
61 is already prime, so the factorization is simply 61.
How is 61 represented in binary and hexadecimal?
61 converts to 111101 in binary and 3D in hexadecimal, which are helpful for computer science applications.
Is 61 a perfect square, cube, or triangular number?
61 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 61?
The digits sum to 7, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.