4002
4002 is a even composite number that follows 4001 and precedes 4003. It is composed of 16 distinct factors: 1, 2, 3, 6, 23, 29, 46, 58, 69, 87, 138, 174, 667, 1334, 2001, 4002. Its prime factorization can be written as 2 × 3 × 23 × 29. 4002 is classified as a abundant number based on the sum of its proper divisors. In computer science, 4002 is represented as 111110100010 in binary and FA2 in hexadecimal.
Factor Analysis
16 FactorsProperties
The prime factorization (2 × 3 × 23 × 29) reveals 4 prime building blocks.
Divisible by 2
4002 ends in 2, so it is even.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 02 are not divisible by 4.
Divisible by 5
4002 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 6 is not a multiple of 9.
Divisible by 10
4002 does not end in 0.
Divisible by 11
The alternating digit sum 2 is not a multiple of 11.
Abundant classification and digit analytics place 4002 within several notable number theory sequences:
Timeline
Deep dive
How 4002 breaks down
4002 carries 16 distinct factors and a digit signature of 6 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 4638, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111110100010 supports bitwise reasoning, hexadecimal FA2 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4002 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4002 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3997–4007) to tune search ranges, and educators feature 4002 in worksheets about factor trees. Its binary footprint of length 12 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 4002 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 4002
Is 4002 a prime number?
4002 is composite with 16 total factors and the prime factorization 2 × 3 × 23 × 29.
What is the prime factorization of 4002?
It breaks down as 2 × 3 × 23 × 29, multiplying the primes 2 × 3 × 23 × 29.
How is 4002 represented in binary and hexadecimal?
4002 converts to 111110100010 in binary and FA2 in hexadecimal, which are helpful for computer science applications.
Is 4002 a perfect square, cube, or triangular number?
4002 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 4002?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.