1040
1040 is a even composite number that follows 1039 and precedes 1041. It is composed of 20 distinct factors: 1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 40, 52, 65, 80, 104, 130, 208, 260, 520, 1040. Its prime factorization can be written as 2^4 × 5 × 13. 1040 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1040 is represented as 10000010000 in binary and 410 in hexadecimal. Historically, it is written as MXL in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 5 × 13) reveals 6 prime building blocks.
Divisible by 2
1040 ends in 0, so it is even.
Divisible by 3
The digit sum 5 is not a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
1040 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 5 is not a multiple of 9.
Divisible by 10
1040 ends in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 1040 within several notable number theory sequences:
Timeline
Deep dive
How 1040 breaks down
1040 carries 20 distinct factors and a digit signature of 5 (5 as the digital root). The abundant classification indicates that its proper divisors sum to 1564, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10000010000 supports bitwise reasoning, hexadecimal 410 aligns with computing notation, and the Roman numeral MXL keeps the encyclopedic tradition alive. These attributes make 1040 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1040 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1035–1045) to tune search ranges, and educators feature 1040 in worksheets about factor trees. Its binary footprint of length 11 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 1040 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 1040
Is 1040 a prime number?
1040 is composite with 20 total factors and the prime factorization 2^4 × 5 × 13.
What is the prime factorization of 1040?
It breaks down as 2^4 × 5 × 13, multiplying the primes 2 × 2 × 2 × 2 × 5 × 13.
How is 1040 represented in binary and hexadecimal?
1040 converts to 10000010000 in binary and 410 in hexadecimal, which are helpful for computer science applications.
Is 1040 a perfect square, cube, or triangular number?
1040 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1040?
The digits sum to 5, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.