36
36 is a even composite number that follows 35 and precedes 37. It is composed of 9 distinct factors: 1, 2, 3, 4, 6, 9, 12, 18, 36. Its prime factorization can be written as 2^2 × 3^2. 36 is classified as a abundant number based on the sum of its proper divisors. In computer science, 36 is represented as 100100 in binary and 24 in hexadecimal. Historically, it is written as XXXVI in Roman numerals. It also belongs to the perfect square, triangular number sequences.
Factor Analysis
9 FactorsProperties
The prime factorization (2^2 × 3^2) reveals 4 prime building blocks.
Divisible by 2
36 ends in 6, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 36 form a multiple of 4.
Divisible by 5
36 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 9 is a multiple of 9.
Divisible by 10
36 does not end in 0.
Divisible by 11
The alternating digit sum -3 is not a multiple of 11.
Abundant classification and digit analytics place 36 within several notable number theory sequences:
Timeline
Deep dive
How 36 breaks down
36 carries 9 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 55, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 100100 supports bitwise reasoning, hexadecimal 24 aligns with computing notation, and the Roman numeral XXXVI keeps the encyclopedic tradition alive. These attributes make 36 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 36 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (31–41) to tune search ranges, and educators feature 36 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, Abundant numbers, Perfect squares, Triangular numbers) help historians, numerologists, and trivia writers tie 36 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 36
Is 36 a prime number?
36 is composite with 9 total factors and the prime factorization 2^2 × 3^2.
What is the prime factorization of 36?
It breaks down as 2^2 × 3^2, multiplying the primes 2 × 2 × 3 × 3.
How is 36 represented in binary and hexadecimal?
36 converts to 100100 in binary and 24 in hexadecimal, which are helpful for computer science applications.
Is 36 a perfect square, cube, or triangular number?
36 is a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 36?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.