63
63 is a odd composite number that follows 62 and precedes 64. It is composed of 6 distinct factors: 1, 3, 7, 9, 21, 63. Its prime factorization can be written as 3^2 × 7. 63 is classified as a deficient number based on the sum of its proper divisors. In computer science, 63 is represented as 111111 in binary and 3F in hexadecimal. Historically, it is written as LXIII in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (3^2 × 7) reveals 3 prime building blocks.
Divisible by 2
63 ends in 3, so it is odd.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 63 are not divisible by 4.
Divisible by 5
63 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 9 is a multiple of 9.
Divisible by 10
63 does not end in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Deficient classification and digit analytics place 63 within several notable number theory sequences:
Timeline
Deep dive
How 63 breaks down
63 carries 6 distinct factors and a digit signature of 9 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 41, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111111 supports bitwise reasoning, hexadecimal 3F aligns with computing notation, and the Roman numeral LXIII keeps the encyclopedic tradition alive. These attributes make 63 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 63 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (58–68) to tune search ranges, and educators feature 63 in worksheets about factor trees. 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 (Composite numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 63 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 63
Is 63 a prime number?
63 is composite with 6 total factors and the prime factorization 3^2 × 7.
What is the prime factorization of 63?
It breaks down as 3^2 × 7, multiplying the primes 3 × 3 × 7.
How is 63 represented in binary and hexadecimal?
63 converts to 111111 in binary and 3F in hexadecimal, which are helpful for computer science applications.
Is 63 a perfect square, cube, or triangular number?
63 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 63?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.