117,600

2⁵ × 3 × 5² × 7²

117,600 has digital root 6. The neighboring primes are 117577 and 117617; its proper-divisor sum differs from the starting integer by 210,084.

Prime Factor Structure

Factorization String 2^5 × 3 × 5^2 × 7^2

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 108

Divisor Sum (σ) 445,284

Proper Divisor Sum 327,684

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #117577 ← → #117617

Radix Representation

Decimal	117600
Binary	11100101101100000 (17 bits)
Octal	0o345540
Hexadecimal	0x1CB60

Divisor Catalog (60 of 108)

1 2 3 4 5 6 7 8 10 12 14 15 16 20 21 24 25 28 30 32 35 40 42 48 49 50 56 60 70 75 80 84 96 98 100 105 112 120 140 147 150 160 168 175 196 200 210 224 240 245 280 294 300 336 350 392 400 420 480 490

Collatz Trajectory (105 steps to reach 1)

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

117,600 58,800 29,400 14,700 7,350 3,675 11,026 5,513 16,540 8,270 4,135 12,406 6,203 18,610 9,305 27,916 13,958 6,979 20,938 10,469 31,408 15,704 7,852 3,926 1,963 5,890 2,945 8,836 4,418 2,209 6,628 3,314 1,657 4,972 2,486 1,243 3,730 1,865 5,596 2,798 1,399 4,198 2,099 6,298 3,149 9,448 4,724 2,362 1,181 3,544 1,772 886 443 1,330 665 1,996 998 499 1,498 749

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