3240
3240 is a even composite number that follows 3239 and precedes 3241. It is composed of 40 distinct factors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 270, 324, 360, 405, 540, 648, 810, 1080, 1620, 3240. Its prime factorization can be written as 2^3 × 3^4 × 5. 3240 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3240 is represented as 110010101000 in binary and CA8 in hexadecimal. Historically, it is written as MMMCCXL in Roman numerals. It also belongs to the triangular number sequence.
Factor Analysis
40 FactorsProperties
The prime factorization (2^3 × 3^4 × 5) reveals 8 prime building blocks.
Divisible by 2
3240 ends in 0, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
3240 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 9 is a multiple of 9.
Divisible by 10
3240 ends in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 3240 within several notable number theory sequences:
Timeline
Deep dive
How 3240 breaks down
3240 carries 40 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 7650, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110010101000 supports bitwise reasoning, hexadecimal CA8 aligns with computing notation, and the Roman numeral MMMCCXL keeps the encyclopedic tradition alive. These attributes make 3240 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3240 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3235–3245) to tune search ranges, and educators feature 3240 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, Triangular numbers) help historians, numerologists, and trivia writers tie 3240 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 3240
Is 3240 a prime number?
3240 is composite with 40 total factors and the prime factorization 2^3 × 3^4 × 5.
What is the prime factorization of 3240?
It breaks down as 2^3 × 3^4 × 5, multiplying the primes 2 × 2 × 2 × 3 × 3 × 3 × 3 × 5.
How is 3240 represented in binary and hexadecimal?
3240 converts to 110010101000 in binary and CA8 in hexadecimal, which are helpful for computer science applications.
Is 3240 a perfect square, cube, or triangular number?
3240 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 3240?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.