75
75 is a odd composite number that follows 74 and precedes 76. It is composed of 6 distinct factors: 1, 3, 5, 15, 25, 75. Its prime factorization can be written as 3 × 5^2. 75 is classified as a deficient number based on the sum of its proper divisors. In computer science, 75 is represented as 1001011 in binary and 4B in hexadecimal. Historically, it is written as LXXV in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (3 × 5^2) reveals 3 prime building blocks.
Divisible by 2
75 ends in 5, so it is odd.
Divisible by 3
The digit sum 12 is a multiple of 3.
Divisible by 4
The last two digits 75 are not divisible by 4.
Divisible by 5
75 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 12 is not a multiple of 9.
Divisible by 10
75 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Deficient classification and digit analytics place 75 within several notable number theory sequences:
Timeline
Deep dive
How 75 breaks down
75 carries 6 distinct factors and a digit signature of 12 (3 as the digital root). The deficient classification indicates that its proper divisors sum to 49, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1001011 supports bitwise reasoning, hexadecimal 4B aligns with computing notation, and the Roman numeral LXXV keeps the encyclopedic tradition alive. These attributes make 75 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 75 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (70–80) to tune search ranges, and educators feature 75 in worksheets about factor trees. Its binary footprint of length 7 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 75 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 75
Is 75 a prime number?
75 is composite with 6 total factors and the prime factorization 3 × 5^2.
What is the prime factorization of 75?
It breaks down as 3 × 5^2, multiplying the primes 3 × 5 × 5.
How is 75 represented in binary and hexadecimal?
75 converts to 1001011 in binary and 4B in hexadecimal, which are helpful for computer science applications.
Is 75 a perfect square, cube, or triangular number?
75 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 75?
The digits sum to 12, producing a digital root of 3. These tests power divisibility shortcuts for 3 and 9.