3472
3472 is a even composite number that follows 3471 and precedes 3473. It is composed of 20 distinct factors: 1, 2, 4, 7, 8, 14, 16, 28, 31, 56, 62, 112, 124, 217, 248, 434, 496, 868, 1736, 3472. Its prime factorization can be written as 2^4 × 7 × 31. 3472 is classified as a abundant number based on the sum of its proper divisors. In computer science, 3472 is represented as 110110010000 in binary and D90 in hexadecimal. Historically, it is written as MMMCDLXXII in Roman numerals.
Factor Analysis
20 FactorsProperties
The prime factorization (2^4 × 7 × 31) reveals 6 prime building blocks.
Divisible by 2
3472 ends in 2, so it is even.
Divisible by 3
The digit sum 16 is not a multiple of 3.
Divisible by 4
The last two digits 72 form a multiple of 4.
Divisible by 5
3472 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
3472 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 3472 within several notable number theory sequences:
Timeline
Deep dive
How 3472 breaks down
3472 carries 20 distinct factors and a digit signature of 16 (7 as the digital root). The abundant classification indicates that its proper divisors sum to 4464, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110110010000 supports bitwise reasoning, hexadecimal D90 aligns with computing notation, and the Roman numeral MMMCDLXXII keeps the encyclopedic tradition alive. These attributes make 3472 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 3472 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3467–3477) to tune search ranges, and educators feature 3472 in worksheets about factor trees. 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 (Composite numbers, Abundant numbers) help historians, numerologists, and trivia writers tie 3472 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 3472
Is 3472 a prime number?
3472 is composite with 20 total factors and the prime factorization 2^4 × 7 × 31.
What is the prime factorization of 3472?
It breaks down as 2^4 × 7 × 31, multiplying the primes 2 × 2 × 2 × 2 × 7 × 31.
How is 3472 represented in binary and hexadecimal?
3472 converts to 110110010000 in binary and D90 in hexadecimal, which are helpful for computer science applications.
Is 3472 a perfect square, cube, or triangular number?
3472 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 3472?
The digits sum to 16, producing a digital root of 7. These tests power divisibility shortcuts for 3 and 9.