402
402 is a even composite number that follows 401 and precedes 403. It is composed of 8 distinct factors: 1, 2, 3, 6, 67, 134, 201, 402. Its prime factorization can be written as 2 × 3 × 67. 402 is classified as a abundant number based on the sum of its proper divisors. In computer science, 402 is represented as 110010010 in binary and 192 in hexadecimal. Historically, it is written as CDII in Roman numerals.
Factor Analysis
8 FactorsProperties
The prime factorization (2 × 3 × 67) reveals 3 prime building blocks.
Divisible by 2
402 ends in 2, so it is even.
Divisible by 3
The digit sum 6 is a multiple of 3.
Divisible by 4
The last two digits 02 are not divisible by 4.
Divisible by 5
402 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 6 is not a multiple of 9.
Divisible by 10
402 does not end in 0.
Divisible by 11
The alternating digit sum 6 is not a multiple of 11.
Abundant classification and digit analytics place 402 within several notable number theory sequences:
Timeline
Deep dive
How 402 breaks down
402 carries 8 distinct factors and a digit signature of 6 (6 as the digital root). The abundant classification indicates that its proper divisors sum to 414, which exceeds the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 110010010 supports bitwise reasoning, hexadecimal 192 aligns with computing notation, and the Roman numeral CDII keeps the encyclopedic tradition alive. These attributes make 402 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 402 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (397–407) to tune search ranges, and educators feature 402 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, Abundant numbers) help historians, numerologists, and trivia writers tie 402 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 402
Is 402 a prime number?
402 is composite with 8 total factors and the prime factorization 2 × 3 × 67.
What is the prime factorization of 402?
It breaks down as 2 × 3 × 67, multiplying the primes 2 × 3 × 67.
How is 402 represented in binary and hexadecimal?
402 converts to 110010010 in binary and 192 in hexadecimal, which are helpful for computer science applications.
Is 402 a perfect square, cube, or triangular number?
402 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 402?
The digits sum to 6, producing a digital root of 6. These tests power divisibility shortcuts for 3 and 9.