3967
3967 is a odd prime number that follows 3966 and precedes 3968. As a prime number, 3967 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 3967. 3967 is classified as a deficient number based on the sum of its proper divisors. In computer science, 3967 is represented as 111101111111 in binary and F7F in hexadecimal. Historically, it is written as MMMCMLXVII in Roman numerals.
Factor Analysis
2 FactorsProperties
3967 is prime, so its only factors are 1 and 3967.
Divisible by 2
3967 ends in 7, so it is odd.
Divisible by 3
The digit sum 25 is not a multiple of 3.
Divisible by 4
The last two digits 67 are not divisible by 4.
Divisible by 5
3967 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 25 is not a multiple of 9.
Divisible by 10
3967 does not end in 0.
Divisible by 11
The alternating digit sum -7 is not a multiple of 11.
Deficient classification and digit analytics place 3967 within several notable number theory sequences:
Timeline
Deep dive
How 3967 breaks down
3967 carries 2 distinct factors and a digit signature of 25 (7 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 111101111111 supports bitwise reasoning, hexadecimal F7F aligns with computing notation, and the Roman numeral MMMCMLXVII keeps the encyclopedic tradition alive. These attributes make 3967 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3967 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3962–3972) to tune search ranges, and educators feature 3967 in worksheets about prime identification. Its binary footprint of length 12 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 3967 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 3967
Is 3967 a prime number?
3967 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 3967?
3967 is already prime, so the factorization is simply 3967.
How is 3967 represented in binary and hexadecimal?
3967 converts to 111101111111 in binary and F7F in hexadecimal, which are helpful for computer science applications.
Is 3967 a perfect square, cube, or triangular number?
3967 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3967?
The digits sum to 25, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.