1251
1251 is a odd composite number that follows 1250 and precedes 1252. It is composed of 6 distinct factors: 1, 3, 9, 139, 417, 1251. Its prime factorization can be written as 3^2 × 139. 1251 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1251 is represented as 10011100011 in binary and 4E3 in hexadecimal. Historically, it is written as MCCLI in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (3^2 × 139) reveals 3 prime building blocks.
Divisible by 2
1251 ends in 1, so it is odd.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 51 are not divisible by 4.
Divisible by 5
1251 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
1251 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 1251 within several notable number theory sequences:
Timeline
Deep dive
How 1251 breaks down
1251 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 569, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10011100011 supports bitwise reasoning, hexadecimal 4E3 aligns with computing notation, and the Roman numeral MCCLI keeps the encyclopedic tradition alive. These attributes make 1251 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1251 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1246–1256) to tune search ranges, and educators feature 1251 in worksheets about factor trees. Its binary footprint of length 11 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 1251 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 1251
Is 1251 a prime number?
1251 is composite with 6 total factors and the prime factorization 3^2 × 139.
What is the prime factorization of 1251?
It breaks down as 3^2 × 139, multiplying the primes 3 × 3 × 139.
How is 1251 represented in binary and hexadecimal?
1251 converts to 10011100011 in binary and 4E3 in hexadecimal, which are helpful for computer science applications.
Is 1251 a perfect square, cube, or triangular number?
1251 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1251?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.