1264
1264 is a even composite number that follows 1263 and precedes 1265. It is composed of 10 distinct factors: 1, 2, 4, 8, 16, 79, 158, 316, 632, 1264. Its prime factorization can be written as 2^4 × 79. 1264 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1264 is represented as 10011110000 in binary and 4F0 in hexadecimal. Historically, it is written as MCCLXIV in Roman numerals.
Factor Analysis
10 FactorsProperties
The prime factorization (2^4 × 79) reveals 5 prime building blocks.
Divisible by 2
1264 ends in 4, so it is even.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
1264 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 13 is not a multiple of 9.
Divisible by 10
1264 does not end in 0.
Divisible by 11
The alternating digit sum 1 is not a multiple of 11.
Deficient classification and digit analytics place 1264 within several notable number theory sequences:
Timeline
Deep dive
How 1264 breaks down
1264 carries 10 distinct factors and a digit signature of 13 (4 as the digital root). The deficient classification indicates that its proper divisors sum to 1216, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 10011110000 supports bitwise reasoning, hexadecimal 4F0 aligns with computing notation, and the Roman numeral MCCLXIV keeps the encyclopedic tradition alive. These attributes make 1264 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1264 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1259–1269) to tune search ranges, and educators feature 1264 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, Deficient numbers) help historians, numerologists, and trivia writers tie 1264 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 1264
Is 1264 a prime number?
1264 is composite with 10 total factors and the prime factorization 2^4 × 79.
What is the prime factorization of 1264?
It breaks down as 2^4 × 79, multiplying the primes 2 × 2 × 2 × 2 × 79.
How is 1264 represented in binary and hexadecimal?
1264 converts to 10011110000 in binary and 4F0 in hexadecimal, which are helpful for computer science applications.
Is 1264 a perfect square, cube, or triangular number?
1264 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1264?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.