7974
7974 is a even composite number that follows 7973 and precedes 7975. It is composed of 12 distinct factors: 1, 2, 3, 6, 9, 18, 443, 886, 1329, 2658, 3987, 7974. Its prime factorization can be written as 2 × 3^2 × 443. 7974 is classified as a abundant number based on the sum of its proper divisors. In computer science, 7974 is represented as 1111100100110 in binary and 1F26 in hexadecimal.
Factor Analysis
12 FactorsProperties
The prime factorization (2 × 3^2 × 443) reveals 4 prime building blocks.
Divisible by 2
7974 ends in 4, so it is even.
Divisible by 3
The digit sum 27 is a multiple of 3.
Divisible by 4
The last two digits 74 are not divisible by 4.
Divisible by 5
7974 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 27 is a multiple of 9.
Divisible by 10
7974 does not end in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Abundant classification and digit analytics place 7974 within several notable number theory sequences:
Timeline
Deep dive
How 7974 breaks down
7974 carries 12 distinct factors and a digit signature of 27 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 9342, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111100100110 supports bitwise reasoning, hexadecimal 1F26 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7974 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7974 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7969–7979) to tune search ranges, and educators feature 7974 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, Abundant numbers) help historians, numerologists, and trivia writers tie 7974 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 7974
Is 7974 a prime number?
7974 is composite with 12 total factors and the prime factorization 2 × 3^2 × 443.
What is the prime factorization of 7974?
It breaks down as 2 × 3^2 × 443, multiplying the primes 2 × 3 × 3 × 443.
How is 7974 represented in binary and hexadecimal?
7974 converts to 1111100100110 in binary and 1F26 in hexadecimal, which are helpful for computer science applications.
Is 7974 a perfect square, cube, or triangular number?
7974 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 7974?
The digits sum to 27, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.