4000
4000 is a even composite number that follows 3999 and precedes 4001. It is composed of 24 distinct factors: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000. Its prime factorization can be written as 2^5 × 5^3. 4000 is classified as a abundant number based on the sum of its proper divisors. In computer science, 4000 is represented as 111110100000 in binary and FA0 in hexadecimal.
Factor Analysis
24 FactorsProperties
The prime factorization (2^5 × 5^3) reveals 8 prime building blocks.
Divisible by 2
4000 ends in 0, so it is even.
Divisible by 3
The digit sum 4 is not a multiple of 3.
Divisible by 4
The last two digits 00 form a multiple of 4.
Divisible by 5
4000 ends in 0, so it is divisible by 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 4 is not a multiple of 9.
Divisible by 10
4000 ends in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Abundant classification and digit analytics place 4000 within several notable number theory sequences:
Timeline
Deep dive
How 4000 breaks down
4000 carries 24 distinct factors and a digit signature of 4 (4 as the digital root). The abundant classification indicates that its proper divisors sum to 5828, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111110100000 supports bitwise reasoning, hexadecimal FA0 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4000 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4000 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3995–4005) to tune search ranges, and educators feature 4000 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 4000 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 4000
Is 4000 a prime number?
4000 is composite with 24 total factors and the prime factorization 2^5 × 5^3.
What is the prime factorization of 4000?
It breaks down as 2^5 × 5^3, multiplying the primes 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5.
How is 4000 represented in binary and hexadecimal?
4000 converts to 111110100000 in binary and FA0 in hexadecimal, which are helpful for computer science applications.
Is 4000 a perfect square, cube, or triangular number?
4000 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 4000?
The digits sum to 4, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.