137
137 is a odd prime number that follows 136 and precedes 138. As a prime number, 137 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 137. 137 is classified as a deficient number based on the sum of its proper divisors. In computer science, 137 is represented as 10001001 in binary and 89 in hexadecimal. Historically, it is written as CXXXVII in Roman numerals.
Factor Analysis
2 FactorsProperties
137 is prime, so its only factors are 1 and 137.
Divisible by 2
137 ends in 7, so it is odd.
Divisible by 3
The digit sum 11 is not a multiple of 3.
Divisible by 4
The last two digits 37 are not divisible by 4.
Divisible by 5
137 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 11 is not a multiple of 9.
Divisible by 10
137 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 137 within several notable number theory sequences:
Timeline
Deep dive
How 137 breaks down
137 carries 2 distinct factors and a digit signature of 11 (2 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 10001001 supports bitwise reasoning, hexadecimal 89 aligns with computing notation, and the Roman numeral CXXXVII keeps the encyclopedic tradition alive. These attributes make 137 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 137 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (132–142) to tune search ranges, and educators feature 137 in worksheets about prime identification. Its binary footprint of length 8 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 137 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 137
Is 137 a prime number?
137 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 137?
137 is already prime, so the factorization is simply 137.
How is 137 represented in binary and hexadecimal?
137 converts to 10001001 in binary and 89 in hexadecimal, which are helpful for computer science applications.
Is 137 a perfect square, cube, or triangular number?
137 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 137?
The digits sum to 11, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.