975
975 is a odd composite number that follows 974 and precedes 976. It is composed of 12 distinct factors: 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975. Its prime factorization can be written as 3 × 5^2 × 13. 975 is classified as a deficient number based on the sum of its proper divisors. In computer science, 975 is represented as 1111001111 in binary and 3CF in hexadecimal. Historically, it is written as CMLXXV in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (3 × 5^2 × 13) reveals 4 prime building blocks.
Divisible by 2
975 ends in 5, so it is odd.
Divisible by 3
The digit sum 21 is a multiple of 3.
Divisible by 4
The last two digits 75 are not divisible by 4.
Divisible by 5
975 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 21 is not a multiple of 9.
Divisible by 10
975 does not end in 0.
Divisible by 11
The alternating digit sum 7 is not a multiple of 11.
Deficient classification and digit analytics place 975 within several notable number theory sequences:
Timeline
Deep dive
How 975 breaks down
975 carries 12 distinct factors and a digit signature of 21 (3 as the digital root). The deficient classification indicates that its proper divisors sum to 761, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111001111 supports bitwise reasoning, hexadecimal 3CF aligns with computing notation, and the Roman numeral CMLXXV keeps the encyclopedic tradition alive. These attributes make 975 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 975 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (970–980) to tune search ranges, and educators feature 975 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, Deficient numbers) help historians, numerologists, and trivia writers tie 975 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 975
Is 975 a prime number?
975 is composite with 12 total factors and the prime factorization 3 × 5^2 × 13.
What is the prime factorization of 975?
It breaks down as 3 × 5^2 × 13, multiplying the primes 3 × 5 × 5 × 13.
How is 975 represented in binary and hexadecimal?
975 converts to 1111001111 in binary and 3CF in hexadecimal, which are helpful for computer science applications.
Is 975 a perfect square, cube, or triangular number?
975 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 975?
The digits sum to 21, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.