3720
3720 is a even composite number that follows 3719 and precedes 3721. It is composed of 32 distinct factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 31, 40, 60, 62, 93, 120, 124, 155, 186, 248, 310, 372, 465, 620, 744, 930, 1240, 1860, 3720. Its prime factorization can be written as 2^3 × 3 × 5 × 31. 3720 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3720 is represented as 111010001000 in binary and E88 in hexadecimal. Historically, it is written as MMMDCCXX in Roman numerals.
Factor Analysis
32 FactorsProperties
The prime factorization (2^3 × 3 × 5 × 31) reveals 6 prime building blocks.
Divisible by 2
3720 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 20 form a multiple of 4.
Divisible by 5
3720 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
3720 ends in 0.
Divisible by 11
The alternating digit sum -2 is not a multiple of 11.
Abundant classification and digit analytics place 3720 within several notable number theory sequences:
Timeline
Deep dive
How 3720 breaks down
3720 carries 32 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 7800, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111010001000 supports bitwise reasoning, hexadecimal E88 aligns with computing notation, and the Roman numeral MMMDCCXX keeps the encyclopedic tradition alive. These attributes make 3720 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3720 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3715–3725) to tune search ranges, and educators feature 3720 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 3720 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 3720
Is 3720 a prime number?
3720 is composite with 32 total factors and the prime factorization 2^3 × 3 × 5 × 31.
What is the prime factorization of 3720?
It breaks down as 2^3 × 3 × 5 × 31, multiplying the primes 2 × 2 × 2 × 3 × 5 × 31.
How is 3720 represented in binary and hexadecimal?
3720 converts to 111010001000 in binary and E88 in hexadecimal, which are helpful for computer science applications.
Is 3720 a perfect square, cube, or triangular number?
3720 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3720?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.