7772
7772 is a even composite number that follows 7771 and precedes 7773. It is composed of 12 distinct factors: 1, 2, 4, 29, 58, 67, 116, 134, 268, 1943, 3886, 7772. Its prime factorization can be written as 2^2 × 29 × 67. 7772 is classified as a deficient number based on the sum of its proper divisors. In computer science, 7772 is represented as 1111001011100 in binary and 1E5C in hexadecimal.
Factor Analysis
12 FactorsProperties
The prime factorization (2^2 × 29 × 67) reveals 4 prime building blocks.
Divisible by 2
7772 ends in 2, so it is even.
Divisible by 3
The digit sum 23 is not a multiple of 3.
Divisible by 4
The last two digits 72 form a multiple of 4.
Divisible by 5
7772 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 23 is not a multiple of 9.
Divisible by 10
7772 does not end in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Deficient classification and digit analytics place 7772 within several notable number theory sequences:
Timeline
Deep dive
How 7772 breaks down
7772 carries 12 distinct factors and a digit signature of 23 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 6508, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111001011100 supports bitwise reasoning, hexadecimal 1E5C aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7772 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7772 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7767–7777) to tune search ranges, and educators feature 7772 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, Deficient numbers) help historians, numerologists, and trivia writers tie 7772 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 7772
Is 7772 a prime number?
7772 is composite with 12 total factors and the prime factorization 2^2 × 29 × 67.
What is the prime factorization of 7772?
It breaks down as 2^2 × 29 × 67, multiplying the primes 2 × 2 × 29 × 67.
How is 7772 represented in binary and hexadecimal?
7772 converts to 1111001011100 in binary and 1E5C in hexadecimal, which are helpful for computer science applications.
Is 7772 a perfect square, cube, or triangular number?
7772 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 7772?
The digits sum to 23, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.