1170
1170 is a even composite number that follows 1169 and precedes 1171. It is composed of 24 distinct factors: 1, 2, 3, 5, 6, 9, 10, 13, 15, 18, 26, 30, 39, 45, 65, 78, 90, 117, 130, 195, 234, 390, 585, 1170. Its prime factorization can be written as 2 × 3^2 × 5 × 13. 1170 is classified as a abundant number based on the sum of its proper divisors. In computer science, 1170 is represented as 10010010010 in binary and 492 in hexadecimal. Historically, it is written as MCLXX in Roman numerals.
Factor Analysis
24 FactorsProperties
The prime factorization (2 × 3^2 × 5 × 13) reveals 5 prime building blocks.
Divisible by 2
1170 ends in 0, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 70 are not divisible by 4.
Divisible by 5
1170 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 9 is a multiple of 9.
Divisible by 10
1170 ends in 0.
Divisible by 11
The alternating digit sum 7 is not a multiple of 11.
Abundant classification and digit analytics place 1170 within several notable number theory sequences:
Timeline
Deep dive
How 1170 breaks down
1170 carries 24 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 2106, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10010010010 supports bitwise reasoning, hexadecimal 492 aligns with computing notation, and the Roman numeral MCLXX keeps the encyclopedic tradition alive. These attributes make 1170 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1170 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1165–1175) to tune search ranges, and educators feature 1170 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 1170 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 1170
Is 1170 a prime number?
1170 is composite with 24 total factors and the prime factorization 2 × 3^2 × 5 × 13.
What is the prime factorization of 1170?
It breaks down as 2 × 3^2 × 5 × 13, multiplying the primes 2 × 3 × 3 × 5 × 13.
How is 1170 represented in binary and hexadecimal?
1170 converts to 10010010010 in binary and 492 in hexadecimal, which are helpful for computer science applications.
Is 1170 a perfect square, cube, or triangular number?
1170 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1170?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.