2964
2964 is a even composite number that follows 2963 and precedes 2965. It is composed of 24 distinct factors: 1, 2, 3, 4, 6, 12, 13, 19, 26, 38, 39, 52, 57, 76, 78, 114, 156, 228, 247, 494, 741, 988, 1482, 2964. Its prime factorization can be written as 2^2 × 3 × 13 × 19. 2964 is classified as a abundant number based on the sum of its proper divisors. In computer science, 2964 is represented as 101110010100 in binary and B94 in hexadecimal. Historically, it is written as MMCMLXIV in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2^2 × 3 × 13 × 19) reveals 5 prime building blocks.
Divisible by 2
2964 ends in 4, so it is even.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
2964 does not end in 0 or 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 21 is not a multiple of 9.
Divisible by 10
2964 does not end in 0.
Divisible by 11
The alternating digit sum -5 is not a multiple of 11.
Abundant classification and digit analytics place 2964 within several notable number theory sequences:
Timeline
Deep dive
How 2964 breaks down
2964 carries 24 distinct factors and a digit signature of 21 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 4876, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 101110010100 supports bitwise reasoning, hexadecimal B94 aligns with computing notation, and the Roman numeral MMCMLXIV keeps the encyclopedic tradition alive. These attributes make 2964 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 2964 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (2959–2969) to tune search ranges, and educators feature 2964 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 2964 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 2964
Is 2964 a prime number?
2964 is composite with 24 total factors and the prime factorization 2^2 × 3 × 13 × 19.
What is the prime factorization of 2964?
It breaks down as 2^2 × 3 × 13 × 19, multiplying the primes 2 × 2 × 3 × 13 × 19.
How is 2964 represented in binary and hexadecimal?
2964 converts to 101110010100 in binary and B94 in hexadecimal, which are helpful for computer science applications.
Is 2964 a perfect square, cube, or triangular number?
2964 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 2964?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.