472
472 is a even composite number that follows 471 and precedes 473. It is composed of 8 distinct factors: 1, 2, 4, 8, 59, 118, 236, 472. Its prime factorization can be written as 2^3 × 59. 472 is classified as a deficient number based on the sum of its proper divisors. In computer science, 472 is represented as 111011000 in binary and 1D8 in hexadecimal. Historically, it is written as CDLXXII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2^3 × 59) reveals 4 prime building blocks.
Divisible by 2
472 ends in 2, so it is even.
Divisible by 3
The digit sum 13 is not a multiple of 3.
Divisible by 4
The last two digits 72 form a multiple of 4.
Divisible by 5
472 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 13 is not a multiple of 9.
Divisible by 10
472 does not end in 0.
Divisible by 11
The alternating digit sum -1 is not a multiple of 11.
Deficient classification and digit analytics place 472 within several notable number theory sequences:
Timeline
Deep dive
How 472 breaks down
472 carries 8 distinct factors and a digit signature of 13 (4 as the digital root). The deficient classification indicates that its proper divisors sum to 428, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111011000 supports bitwise reasoning, hexadecimal 1D8 aligns with computing notation, and the Roman numeral CDLXXII keeps the encyclopedic tradition alive. These attributes make 472 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 472 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (467–477) to tune search ranges, and educators feature 472 in worksheets about factor trees. Its binary footprint of length 9 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Composite numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 472 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 472
Is 472 a prime number?
472 is composite with 8 total factors and the prime factorization 2^3 × 59.
What is the prime factorization of 472?
It breaks down as 2^3 × 59, multiplying the primes 2 × 2 × 2 × 59.
How is 472 represented in binary and hexadecimal?
472 converts to 111011000 in binary and 1D8 in hexadecimal, which are helpful for computer science applications.
Is 472 a perfect square, cube, or triangular number?
472 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 472?
The digits sum to 13, producing a digital root of 4. These tests power divisibility shortcuts for 3 and 9.