972
972 is a even composite number that follows 971 and precedes 973. It is composed of 18 distinct factors: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972. Its prime factorization can be written as 2^2 × 3^5. 972 is classified as a abundant number based on the sum of its proper divisors. In computer science, 972 is represented as 1111001100 in binary and 3CC in hexadecimal. Historically, it is written as CMLXXII in Roman numerals.
Factor Analysis
18 FactorsProperties
The prime factorization (2^2 × 3^5) reveals 7 prime building blocks.
Divisible by 2
972 ends in 2, so it is even.
Divisible by 3
The digit sum 18 is a multiple of 3.
Divisible by 4
The last two digits 72 form a multiple of 4.
Divisible by 5
972 does not end in 0 or 5.
Divisible by 6
It meets the tests for both 2 and 3, so it is divisible by 6.
Divisible by 9
The digit sum 18 is a multiple of 9.
Divisible by 10
972 does not end in 0.
Divisible by 11
The alternating digit sum 4 is not a multiple of 11.
Abundant classification and digit analytics place 972 within several notable number theory sequences:
Timeline
Deep dive
How 972 breaks down
972 carries 18 distinct factors and a digit signature of 18 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 1576, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1111001100 supports bitwise reasoning, hexadecimal 3CC aligns with computing notation, and the Roman numeral CMLXXII keeps the encyclopedic tradition alive. These attributes make 972 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 972 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (967–977) to tune search ranges, and educators feature 972 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, Abundant numbers) help historians, numerologists, and trivia writers tie 972 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 972
Is 972 a prime number?
972 is composite with 18 total factors and the prime factorization 2^2 × 3^5.
What is the prime factorization of 972?
It breaks down as 2^2 × 3^5, multiplying the primes 2 × 2 × 3 × 3 × 3 × 3 × 3.
How is 972 represented in binary and hexadecimal?
972 converts to 1111001100 in binary and 3CC in hexadecimal, which are helpful for computer science applications.
Is 972 a perfect square, cube, or triangular number?
972 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 972?
The digits sum to 18, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.