1221
1221 is a odd composite number that follows 1220 and precedes 1222. It is composed of 8 distinct factors: 1, 3, 11, 33, 37, 111, 407, 1221. Its prime factorization can be written as 3 × 11 × 37. 1221 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1221 is represented as 10011000101 in binary and 4C5 in hexadecimal. Historically, it is written as MCCXXI in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (3 × 11 × 37) reveals 3 prime building blocks.
Divisible by 2
1221 ends in 1, so it is odd.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 21 are not divisible by 4.
Divisible by 5
1221 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 6 is not a multiple of 9.
Divisible by 10
1221 does not end in 0.
Divisible by 11
The alternating digit sum 0 is a multiple of 11.
Deficient classification and digit analytics place 1221 within several notable number theory sequences:
Timeline
Deep dive
How 1221 breaks down
1221 carries 8 distinct factors and a digit signature of 6 (6 as the digital root). The deficient classification indicates that its proper divisors sum to 603, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10011000101 supports bitwise reasoning, hexadecimal 4C5 aligns with computing notation, and the Roman numeral MCCXXI keeps the encyclopedic tradition alive. These attributes make 1221 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1221 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1216–1226) to tune search ranges, and educators feature 1221 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 1221 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 1221
Is 1221 a prime number?
1221 is composite with 8 total factors and the prime factorization 3 × 11 × 37.
What is the prime factorization of 1221?
It breaks down as 3 × 11 × 37, multiplying the primes 3 × 11 × 37.
How is 1221 represented in binary and hexadecimal?
1221 converts to 10011000101 in binary and 4C5 in hexadecimal, which are helpful for computer science applications.
Is 1221 a perfect square, cube, or triangular number?
1221 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1221?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.