624
624 is a even composite number that follows 623 and precedes 625. It is composed of 20 distinct factors: 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624. Its prime factorization can be written as 2^4 × 3 × 13. 624 is classified as a abundant number based on the sum of its proper divisors. In computer science, 624 is represented as 1001110000 in binary and 270 in hexadecimal. Historically, it is written as DCXXIV in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 3 × 13) reveals 6 prime building blocks.
Divisible by 2
624 ends in 4, so it is even.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 24 form a multiple of 4.
Divisible by 5
624 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 12 is not a multiple of 9.
Divisible by 10
624 does not end in 0.
Divisible by 11
The alternating digit sum 8 is not a multiple of 11.
Abundant classification and digit analytics place 624 within several notable number theory sequences:
Timeline
Deep dive
How 624 breaks down
624 carries 20 distinct factors and a digit signature of 12 (3 as the digital root). The abundant classification indicates that its proper divisors sum to 1112, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1001110000 supports bitwise reasoning, hexadecimal 270 aligns with computing notation, and the Roman numeral DCXXIV keeps the encyclopedic tradition alive. These attributes make 624 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 624 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (619–629) to tune search ranges, and educators feature 624 in worksheets about factor trees. Its binary footprint of length 10 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 624 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 624
Is 624 a prime number?
624 is composite with 20 total factors and the prime factorization 2^4 × 3 × 13.
What is the prime factorization of 624?
It breaks down as 2^4 × 3 × 13, multiplying the primes 2 × 2 × 2 × 2 × 3 × 13.
How is 624 represented in binary and hexadecimal?
624 converts to 1001110000 in binary and 270 in hexadecimal, which are helpful for computer science applications.
Is 624 a perfect square, cube, or triangular number?
624 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 624?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.