3760
3760 is a even composite number that follows 3759 and precedes 3761. It is composed of 20 distinct factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 47, 80, 94, 188, 235, 376, 470, 752, 940, 1880, 3760. Its prime factorization can be written as 2^4 × 5 × 47. 3760 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3760 is represented as 111010110000 in binary and EB0 in hexadecimal. Historically, it is written as MMMDCCLX in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 5 × 47) reveals 6 prime building blocks.
Divisible by 2
3760 ends in 0, so it is even.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 60 form a multiple of 4.
Divisible by 5
3760 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 16 is not a multiple of 9.
Divisible by 10
3760 ends in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 3760 within several notable number theory sequences:
Timeline
Deep dive
How 3760 breaks down
3760 carries 20 distinct factors and a digit signature of 16 (7 as the digital root). The abundant classification indicates that its proper divisors sum to 5168, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111010110000 supports bitwise reasoning, hexadecimal EB0 aligns with computing notation, and the Roman numeral MMMDCCLX keeps the encyclopedic tradition alive. These attributes make 3760 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3760 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3755–3765) to tune search ranges, and educators feature 3760 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 3760 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 3760
Is 3760 a prime number?
3760 is composite with 20 total factors and the prime factorization 2^4 × 5 × 47.
What is the prime factorization of 3760?
It breaks down as 2^4 × 5 × 47, multiplying the primes 2 × 2 × 2 × 2 × 5 × 47.
How is 3760 represented in binary and hexadecimal?
3760 converts to 111010110000 in binary and EB0 in hexadecimal, which are helpful for computer science applications.
Is 3760 a perfect square, cube, or triangular number?
3760 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3760?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.