72
72 is a even composite number that follows 71 and precedes 73. It is composed of 12 distinct factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Its prime factorization can be written as 2^3 × 3^2. 72 is classified as a abundant number based on the sum of its proper divisors. In computer science, 72 is represented as 1001000 in binary and 48 in hexadecimal. Historically, it is written as LXXII in Roman numerals.
Factor Analysis
12 FactorsProperties
The prime factorization (2^3 × 3^2) reveals 5 prime building blocks.
Divisible by 2
72 ends in 2, so it is even.
Divisible by 3
The digit sum 9 is a multiple of 3.
Divisible by 4
The last two digits 72 form a multiple of 4.
Divisible by 5
72 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 9 is a multiple of 9.
Divisible by 10
72 does not end in 0.
Divisible by 11
The alternating digit sum 5 is not a multiple of 11.
Abundant classification and digit analytics place 72 within several notable number theory sequences:
Timeline
Deep dive
How 72 breaks down
72 carries 12 distinct factors and a digit signature of 9 (9 as the digital root). The abundant classification indicates that its proper divisors sum to 123, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 1001000 supports bitwise reasoning, hexadecimal 48 aligns with computing notation, and the Roman numeral LXXII keeps the encyclopedic tradition alive. These attributes make 72 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 72 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (67–77) to tune search ranges, and educators feature 72 in worksheets about factor trees. Its binary footprint of length 7 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 72 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 72
Is 72 a prime number?
72 is composite with 12 total factors and the prime factorization 2^3 × 3^2.
What is the prime factorization of 72?
It breaks down as 2^3 × 3^2, multiplying the primes 2 × 2 × 2 × 3 × 3.
How is 72 represented in binary and hexadecimal?
72 converts to 1001000 in binary and 48 in hexadecimal, which are helpful for computer science applications.
Is 72 a perfect square, cube, or triangular number?
72 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 72?
The digits sum to 9, producing a digital root of 9. These tests power divisibility shortcuts for 3 and 9.