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Modular Archive

180,084

22 × 3 × 43 × 349
Abundant Even Composite

The decimal integer 180,084 is 101011111101110100 in binary (18 bits), 537564 in octal and 2BF74 in hexadecimal. Its digit sum is 21.

Prime Factor Structure

Factorization String 2^2 × 3 × 43 × 349
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 24
Divisor Sum (σ) 431,200
Proper Divisor Sum 251,116
Digit Sum / Digital Root 21 (Root: 3)
Adjacent Primes #180077 ← → #180097

Radix Representation

Decimal 180084
Binary 101011111101110100 (18 bits)
Octal 0o537564
Hexadecimal 0x2BF74

Divisor Catalog (24)

1 2 3 4 6 12 43 86 129 172 258 349 516 698 1,047 1,396 2,094 4,188 15,007 30,014 45,021 60,028 90,042 180,084

Collatz Trajectory (64 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

180,084 90,042 45,021 135,064 67,532 33,766 16,883 50,650 25,325 75,976 37,988 18,994 9,497 28,492 14,246 7,123 21,370 10,685 32,056 16,028 8,014 4,007 12,022 6,011 18,034 9,017 27,052 13,526 6,763 20,290 10,145 30,436 15,218 7,609 22,828 11,414 5,707 17,122 8,561 25,684 12,842 6,421 19,264 9,632 4,816 2,408 1,204 602 301 904 452 226 113 340 170 85 256 128 64 32

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