967
967 is a odd prime number that follows 966 and precedes 968. As a prime number, 967 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 967. 967 is classified as a deficient number based on the sum of its proper divisors. In computer science, 967 is represented as 1111000111 in binary and 3C7 in hexadecimal. Historically, it is written as CMLXVII in Roman numerals.
Factor Analysis
2 FactorsProperties
967 is prime, so its only factors are 1 and 967.
Divisible by 2
967 ends in 7, so it is odd.
Divisible by 3
The digit sum 22 is not a multiple of 3.
Divisible by 4
The last two digits 67 are not divisible by 4.
Divisible by 5
967 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 22 is not a multiple of 9.
Divisible by 10
967 does not end in 0.
Divisible by 11
The alternating digit sum 10 is not a multiple of 11.
Deficient classification and digit analytics place 967 within several notable number theory sequences:
Timeline
Deep dive
How 967 breaks down
967 carries 2 distinct factors and a digit signature of 22 (4 as the digital root). The deficient classification indicates that its proper divisors sum to 1, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111000111 supports bitwise reasoning, hexadecimal 3C7 aligns with computing notation, and the Roman numeral CMLXVII keeps the encyclopedic tradition alive. These attributes make 967 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 967 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (962–972) to tune search ranges, and educators feature 967 in worksheets about prime identification. Its binary footprint of length 10 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 967 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 967
Is 967 a prime number?
967 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 967?
967 is already prime, so the factorization is simply 967.
How is 967 represented in binary and hexadecimal?
967 converts to 1111000111 in binary and 3C7 in hexadecimal, which are helpful for computer science applications.
Is 967 a perfect square, cube, or triangular number?
967 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 967?
The digits sum to 22, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.