1629
1629 is a odd composite number that follows 1628 and precedes 1630. It is composed of 6 distinct factors: 1, 3, 9, 181, 543, 1629. Its prime factorization can be written as 3^2 × 181. 1629 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1629 is represented as 11001011101 in binary and 65D in hexadecimal. Historically, it is written as MDCXXIX in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (3^2 × 181) reveals 3 prime building blocks.
Divisible by 2
1629 ends in 9, so it is odd.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 29 are not divisible by 4.
Divisible by 5
1629 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 18 is a multiple of 9.
Divisible by 10
1629 does not end in 0.
Divisible by 11
The alternating digit sum -12 is not a multiple of 11.
Deficient classification and digit analytics place 1629 within several notable number theory sequences:
Timeline
Deep dive
How 1629 breaks down
1629 carries 6 distinct factors and a digit signature of 18 (9 as the digital root). The deficient classification indicates that its proper divisors sum to 737, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11001011101 supports bitwise reasoning, hexadecimal 65D aligns with computing notation, and the Roman numeral MDCXXIX keeps the encyclopedic tradition alive. These attributes make 1629 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1629 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1624–1634) to tune search ranges, and educators feature 1629 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 1629 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 1629
Is 1629 a prime number?
1629 is composite with 6 total factors and the prime factorization 3^2 × 181.
What is the prime factorization of 1629?
It breaks down as 3^2 × 181, multiplying the primes 3 × 3 × 181.
How is 1629 represented in binary and hexadecimal?
1629 converts to 11001011101 in binary and 65D in hexadecimal, which are helpful for computer science applications.
Is 1629 a perfect square, cube, or triangular number?
1629 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1629?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.