37
37 is a odd prime number that follows 36 and precedes 38. As a prime number, 37 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 37. 37 is classified as a deficient number based on the sum of its proper divisors. In computer science, 37 is represented as 100101 in binary and 25 in hexadecimal. Historically, it is written as XXXVII in Roman numerals.
Factor Analysis
2 FactorsProperties
37 is prime, so its only factors are 1 and 37.
Divisible by 2
37 ends in 7, so it is odd.
Divisible by 3
The digit sum 10 is not a multiple of 3.
Divisible by 4
The last two digits 37 are not divisible by 4.
Divisible by 5
37 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 10 is not a multiple of 9.
Divisible by 10
37 does not end in 0.
Divisible by 11
The alternating digit sum -4 is not a multiple of 11.
Deficient classification and digit analytics place 37 within several notable number theory sequences:
Timeline
Deep dive
How 37 breaks down
37 carries 2 distinct factors and a digit signature of 10 (1 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 100101 supports bitwise reasoning, hexadecimal 25 aligns with computing notation, and the Roman numeral XXXVII keeps the encyclopedic tradition alive. These attributes make 37 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 37 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (32–42) to tune search ranges, and educators feature 37 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 37 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 37
Is 37 a prime number?
37 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 37?
37 is already prime, so the factorization is simply 37.
How is 37 represented in binary and hexadecimal?
37 converts to 100101 in binary and 25 in hexadecimal, which are helpful for computer science applications.
Is 37 a perfect square, cube, or triangular number?
37 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 37?
The digits sum to 10, producing a digital root of 1. These tests power divisibility shortcuts for 3 and 9.