7440
7440 is a even composite number that follows 7439 and precedes 7441. It is composed of 40 distinct factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 31, 40, 48, 60, 62, 80, 93, 120, 124, 155, 186, 240, 248, 310, 372, 465, 496, 620, 744, 930, 1240, 1488, 1860, 2480, 3720, 7440. Its prime factorization can be written as 2^4 × 3 × 5 × 31. 7440 is classified as a abundant number based on the sum of its proper divisors. In computer science, 7440 is represented as 1110100010000 in binary and 1D10 in hexadecimal.
Factor Analysis
40 FactorsProperties
The prime factorization (2^4 × 3 × 5 × 31) reveals 7 prime building blocks.
Divisible by 2
7440 ends in 0, so it is even.
Divisible by 3
The digit sum 15 is a multiple of 3.
Divisible by 4
The last two digits 40 form a multiple of 4.
Divisible by 5
7440 ends in 0, so it is divisible by 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 15 is not a multiple of 9.
Divisible by 10
7440 ends in 0.
Divisible by 11
The alternating digit sum 7 is not a multiple of 11.
Abundant classification and digit analytics place 7440 within several notable number theory sequences:
Timeline
Deep dive
How 7440 breaks down
7440 carries 40 distinct factors and a digit signature of 15 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 16368, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1110100010000 supports bitwise reasoning, hexadecimal 1D10 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 7440 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 7440 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (7435–7445) to tune search ranges, and educators feature 7440 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 7440 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 7440
Is 7440 a prime number?
7440 is composite with 40 total factors and the prime factorization 2^4 × 3 × 5 × 31.
What is the prime factorization of 7440?
It breaks down as 2^4 × 3 × 5 × 31, multiplying the primes 2 × 2 × 2 × 2 × 3 × 5 × 31.
How is 7440 represented in binary and hexadecimal?
7440 converts to 1110100010000 in binary and 1D10 in hexadecimal, which are helpful for computer science applications.
Is 7440 a perfect square, cube, or triangular number?
7440 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 7440?
The digits sum to 15, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.