961
961 is a odd composite number that follows 960 and precedes 962. It is composed of 3 distinct factors: 1, 31, 961. Its prime factorization can be written as 31^2. 961 is classified as a deficient number based on the sum of its proper divisors. In computer science, 961 is represented as 1111000001 in binary and 3C1 in hexadecimal. Historically, it is written as CMLXI in Roman numerals. It also belongs to the perfect square sequence.
Factor Analysis
3 FactorsProperties
The prime factorization (31^2) reveals 2 prime building blocks.
Divisible by 2
961 ends in 1, so it is odd.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 61 are not divisible by 4.
Divisible by 5
961 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 16 is not a multiple of 9.
Divisible by 10
961 does not end in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Deficient classification and digit analytics place 961 within several notable number theory sequences:
Timeline
Deep dive
How 961 breaks down
961 carries 3 distinct factors and a digit signature of 16 (7 as the digital root). The deficient classification indicates that its proper divisors sum to 32, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111000001 supports bitwise reasoning, hexadecimal 3C1 aligns with computing notation, and the Roman numeral CMLXI keeps the encyclopedic tradition alive. These attributes make 961 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 961 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (956–966) to tune search ranges, and educators feature 961 in worksheets about factor trees. 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 (Composite numbers, Deficient numbers, Perfect squares) help historians, numerologists, and trivia writers tie 961 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 961
Is 961 a prime number?
961 is composite with 3 total factors and the prime factorization 31^2.
What is the prime factorization of 961?
It breaks down as 31^2, multiplying the primes 31 × 31.
How is 961 represented in binary and hexadecimal?
961 converts to 1111000001 in binary and 3C1 in hexadecimal, which are helpful for computer science applications.
Is 961 a perfect square, cube, or triangular number?
961 is a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 961?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.