3450
3450 is a even composite number that follows 3449 and precedes 3451. It is composed of 24 distinct factors: 1, 2, 3, 5, 6, 10, 15, 23, 25, 30, 46, 50, 69, 75, 115, 138, 150, 230, 345, 575, 690, 1150, 1725, 3450. Its prime factorization can be written as 2 × 3 × 5^2 × 23. 3450 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3450 is represented as 110101111010 in binary and D7A in hexadecimal. Historically, it is written as MMMCDL in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2 × 3 × 5^2 × 23) reveals 5 prime building blocks.
Divisible by 2
3450 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 50 are not divisible by 4.
Divisible by 5
3450 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
3450 ends in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Abundant classification and digit analytics place 3450 within several notable number theory sequences:
Timeline
Deep dive
How 3450 breaks down
3450 carries 24 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 5478, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110101111010 supports bitwise reasoning, hexadecimal D7A aligns with computing notation, and the Roman numeral MMMCDL keeps the encyclopedic tradition alive. These attributes make 3450 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3450 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3445–3455) to tune search ranges, and educators feature 3450 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 3450 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 3450
Is 3450 a prime number?
3450 is composite with 24 total factors and the prime factorization 2 × 3 × 5^2 × 23.
What is the prime factorization of 3450?
It breaks down as 2 × 3 × 5^2 × 23, multiplying the primes 2 × 3 × 5 × 5 × 23.
How is 3450 represented in binary and hexadecimal?
3450 converts to 110101111010 in binary and D7A in hexadecimal, which are helpful for computer science applications.
Is 3450 a perfect square, cube, or triangular number?
3450 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3450?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.