1964
1964 is a even composite number that follows 1963 and precedes 1965. It is composed of 6 distinct factors: 1, 2, 4, 491, 982, 1964. Its prime factorization can be written as 2^2 × 491. 1964 is classified as a deficient number based on the sum of its proper divisors. In computer science, 1964 is represented as 11110101100 in binary and 7AC in hexadecimal. Historically, it is written as MCMLXIV in Roman numerals.
Factor Analysis
6 FactorsProperties
The prime factorization (2^2 × 491) reveals 3 prime building blocks.
Divisible by 2
1964 ends in 4, so it is even.
Divisible by 3
The digit sum 20 is not a multiple of 3.
Divisible by 4
The last two digits 64 form a multiple of 4.
Divisible by 5
1964 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 20 is not a multiple of 9.
Divisible by 10
1964 does not end in 0.
Divisible by 11
The alternating digit sum -6 is not a multiple of 11.
Deficient classification and digit analytics place 1964 within several notable number theory sequences:
Timeline
Deep dive
How 1964 breaks down
1964 carries 6 distinct factors and a digit signature of 20 (2 as the digital root). The deficient classification indicates that its proper divisors sum to 1480, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 11110101100 supports bitwise reasoning, hexadecimal 7AC aligns with computing notation, and the Roman numeral MCMLXIV keeps the encyclopedic tradition alive. These attributes make 1964 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 1964 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (1959–1969) to tune search ranges, and educators feature 1964 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 1964 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 1964
Is 1964 a prime number?
1964 is composite with 6 total factors and the prime factorization 2^2 × 491.
What is the prime factorization of 1964?
It breaks down as 2^2 × 491, multiplying the primes 2 × 2 × 491.
How is 1964 represented in binary and hexadecimal?
1964 converts to 11110101100 in binary and 7AC in hexadecimal, which are helpful for computer science applications.
Is 1964 a perfect square, cube, or triangular number?
1964 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 1964?
The digits sum to 20, producing a digital root of 2. These tests power divisibility shortcuts for 3 and 9.