7875
7875 is a odd composite number that follows 7874 and precedes 7876. It is composed of 24 distinct factors: 1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 125, 175, 225, 315, 375, 525, 875, 1125, 1575, 2625, 7875. Its prime factorization can be written as 3^2 × 5^3 × 7. 7875 is classified as a abundant number based on the sum of its proper divisors. In computer science, 7875 is represented as 1111011000011 in binary and 1EC3 in hexadecimal. It also belongs to the triangular number sequence.
Factor Analysis
24 FactorsProperties
The prime factorization (3^2 × 5^3 × 7) reveals 6 prime building blocks.
Divisible by 2
7875 ends in 5, so it is odd.
Divisible by 3
The digit sum 27 is a multiple of 3.
Divisible by 4
The last two digits 75 are not divisible by 4.
Divisible by 5
7875 ends in 5, 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 27 is a multiple of 9.
Divisible by 10
7875 does not end in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Abundant classification and digit analytics place 7875 within several notable number theory sequences:
Timeline
Deep dive
How 7875 breaks down
7875 carries 24 distinct factors and a digit signature of 27 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 8349, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111011000011 supports bitwise reasoning, hexadecimal 1EC3 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7875 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7875 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7870–7880) to tune search ranges, and educators feature 7875 in worksheets about factor trees. Its binary footprint of length 13 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 7875 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 7875
Is 7875 a prime number?
7875 is composite with 24 total factors and the prime factorization 3^2 × 5^3 × 7.
What is the prime factorization of 7875?
It breaks down as 3^2 × 5^3 × 7, multiplying the primes 3 × 3 × 5 × 5 × 5 × 7.
How is 7875 represented in binary and hexadecimal?
7875 converts to 1111011000011 in binary and 1EC3 in hexadecimal, which are helpful for computer science applications.
Is 7875 a perfect square, cube, or triangular number?
7875 is not a perfect square, is not a perfect cube, and is triangular.
What are the digit sum and digital root of 7875?
The digits sum to 27, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.