3380
3380 is a even composite number that follows 3379 and precedes 3381. It is composed of 18 distinct factors: 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 169, 260, 338, 676, 845, 1690, 3380. Its prime factorization can be written as 2^2 × 5 × 13^2. 3380 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3380 is represented as 110100110100 in binary and D34 in hexadecimal. Historically, it is written as MMMCCCLXXX in Roman numerals.
Factor Analysis
18 FactorsProperties
The prime factorization (2^2 × 5 × 13^2) reveals 5 prime building blocks.
Divisible by 2
3380 ends in 0, so it is even.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 80 form a multiple of 4.
Divisible by 5
3380 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 14 is not a multiple of 9.
Divisible by 10
3380 ends in 0.
Divisible by 11
The alternating digit sum 8 is not a multiple of 11.
Abundant classification and digit analytics place 3380 within several notable number theory sequences:
Timeline
Deep dive
How 3380 breaks down
3380 carries 18 distinct factors and a digit signature of 14 (5 as the digital root). The abundant classification indicates that its proper divisors sum to 4306, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110100110100 supports bitwise reasoning, hexadecimal D34 aligns with computing notation, and the Roman numeral MMMCCCLXXX keeps the encyclopedic tradition alive. These attributes make 3380 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3380 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3375–3385) to tune search ranges, and educators feature 3380 in worksheets about factor trees. Its binary footprint of length 12 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Abundant numbers) help historians, numerologists, and trivia writers tie 3380 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 3380
Is 3380 a prime number?
3380 is composite with 18 total factors and the prime factorization 2^2 × 5 × 13^2.
What is the prime factorization of 3380?
It breaks down as 2^2 × 5 × 13^2, multiplying the primes 2 × 2 × 5 × 13 × 13.
How is 3380 represented in binary and hexadecimal?
3380 converts to 110100110100 in binary and D34 in hexadecimal, which are helpful for computer science applications.
Is 3380 a perfect square, cube, or triangular number?
3380 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3380?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.