3360
3360 is a even composite number that follows 3359 and precedes 3361. It is composed of 48 distinct factors: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 32, 35, 40, 42, 48, 56, 60, 70, 80, 84, 96, 105, 112, 120, 140, 160, 168, 210, 224, 240, 280, 336, 420, 480, 560, 672, 840, 1120, 1680, 3360. Its prime factorization can be written as 2^5 × 3 × 5 × 7. 3360 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3360 is represented as 110100100000 in binary and D20 in hexadecimal. Historically, it is written as MMMCCCLX in Roman numerals.
Factor Analysis
48 FactorsProperties
The prime factorization (2^5 × 3 × 5 × 7) reveals 8 prime building blocks.
Divisible by 2
3360 ends in 0, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 60 form a multiple of 4.
Divisible by 5
3360 ends in 0, so it is divisible by 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 12 is not a multiple of 9.
Divisible by 10
3360 ends in 0.
Divisible by 11
The alternating digit sum 6 is not a multiple of 11.
Abundant classification and digit analytics place 3360 within several notable number theory sequences:
Timeline
Deep dive
How 3360 breaks down
3360 carries 48 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 8736, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110100100000 supports bitwise reasoning, hexadecimal D20 aligns with computing notation, and the Roman numeral MMMCCCLX keeps the encyclopedic tradition alive. These attributes make 3360 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3360 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3355–3365) to tune search ranges, and educators feature 3360 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 3360 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 3360
Is 3360 a prime number?
3360 is composite with 48 total factors and the prime factorization 2^5 × 3 × 5 × 7.
What is the prime factorization of 3360?
It breaks down as 2^5 × 3 × 5 × 7, multiplying the primes 2 × 2 × 2 × 2 × 2 × 3 × 5 × 7.
How is 3360 represented in binary and hexadecimal?
3360 converts to 110100100000 in binary and D20 in hexadecimal, which are helpful for computer science applications.
Is 3360 a perfect square, cube, or triangular number?
3360 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3360?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.