752
752 is a even composite number that follows 751 and precedes 753. It is composed of 10 distinct factors: 1, 2, 4, 8, 16, 47, 94, 188, 376, 752. Its prime factorization can be written as 2^4 × 47. 752 is classified as a deficient number based on the sum of its proper divisors. In computer science, 752 is represented as 1011110000 in binary and 2F0 in hexadecimal. Historically, it is written as DCCLII in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 47) reveals 5 prime building blocks.
Divisible by 2
752 ends in 2, so it is even.
Divisible by 3
The digit sum 14 is not a multiple of 3.
Divisible by 4
The last two digits 52 form a multiple of 4.
Divisible by 5
752 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 14 is not a multiple of 9.
Divisible by 10
752 does not end in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Deficient classification and digit analytics place 752 within several notable number theory sequences:
Timeline
Deep dive
How 752 breaks down
752 carries 10 distinct factors and a digit signature of 14 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 736, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1011110000 supports bitwise reasoning, hexadecimal 2F0 aligns with computing notation, and the Roman numeral DCCLII keeps the encyclopedic tradition alive. These attributes make 752 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 752 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (747–757) to tune search ranges, and educators feature 752 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 752 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 752
Is 752 a prime number?
752 is composite with 10 total factors and the prime factorization 2^4 × 47.
What is the prime factorization of 752?
It breaks down as 2^4 × 47, multiplying the primes 2 × 2 × 2 × 2 × 47.
How is 752 represented in binary and hexadecimal?
752 converts to 1011110000 in binary and 2F0 in hexadecimal, which are helpful for computer science applications.
Is 752 a perfect square, cube, or triangular number?
752 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 752?
The digits sum to 14, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.