3120
3120 is a even composite number that follows 3119 and precedes 3121. It is composed of 40 distinct factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 30, 39, 40, 48, 52, 60, 65, 78, 80, 104, 120, 130, 156, 195, 208, 240, 260, 312, 390, 520, 624, 780, 1040, 1560, 3120. Its prime factorization can be written as 2^4 × 3 × 5 × 13. 3120 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3120 is represented as 110000110000 in binary and C30 in hexadecimal. Historically, it is written as MMMCXX in Roman numerals.
Factor Analysis
40 FactorsProperties
The prime factorization (2^4 × 3 × 5 × 13) reveals 7 prime building blocks.
Divisible by 2
3120 ends in 0, so it is even.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 20 form a multiple of 4.
Divisible by 5
3120 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 6 is not a multiple of 9.
Divisible by 10
3120 ends in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Abundant classification and digit analytics place 3120 within several notable number theory sequences:
Timeline
Deep dive
How 3120 breaks down
3120 carries 40 distinct factors and a digit signature of 6 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 7296, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110000110000 supports bitwise reasoning, hexadecimal C30 aligns with computing notation, and the Roman numeral MMMCXX keeps the encyclopedic tradition alive. These attributes make 3120 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3120 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3115–3125) to tune search ranges, and educators feature 3120 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 3120 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 3120
Is 3120 a prime number?
3120 is composite with 40 total factors and the prime factorization 2^4 × 3 × 5 × 13.
What is the prime factorization of 3120?
It breaks down as 2^4 × 3 × 5 × 13, multiplying the primes 2 × 2 × 2 × 2 × 3 × 5 × 13.
How is 3120 represented in binary and hexadecimal?
3120 converts to 110000110000 in binary and C30 in hexadecimal, which are helpful for computer science applications.
Is 3120 a perfect square, cube, or triangular number?
3120 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3120?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.