762
762 is a even composite number that follows 761 and precedes 763. It is composed of 8 distinct factors: 1, 2, 3, 6, 127, 254, 381, 762. Its prime factorization can be written as 2 × 3 × 127. 762 is classified as a abundant number based on the sum of its proper divisors. In computer science, 762 is represented as 1011111010 in binary and 2FA in hexadecimal. Historically, it is written as DCCLXII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 3 × 127) reveals 3 prime building blocks.
Divisible by 2
762 ends in 2, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 62 are not divisible by 4.
Divisible by 5
762 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 15 is not a multiple of 9.
Divisible by 10
762 does not end in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Abundant classification and digit analytics place 762 within several notable number theory sequences:
Timeline
Deep dive
How 762 breaks down
762 carries 8 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 774, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1011111010 supports bitwise reasoning, hexadecimal 2FA aligns with computing notation, and the Roman numeral DCCLXII keeps the encyclopedic tradition alive. These attributes make 762 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 762 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (757–767) to tune search ranges, and educators feature 762 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 762 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 762
Is 762 a prime number?
762 is composite with 8 total factors and the prime factorization 2 × 3 × 127.
What is the prime factorization of 762?
It breaks down as 2 × 3 × 127, multiplying the primes 2 × 3 × 127.
How is 762 represented in binary and hexadecimal?
762 converts to 1011111010 in binary and 2FA in hexadecimal, which are helpful for computer science applications.
Is 762 a perfect square, cube, or triangular number?
762 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 762?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.