6,115,200

2⁷ × 3 × 5² × 7² × 13

6,115,200 has the prime decomposition 2^7 × 3 × 5^2 × 7^2 × 13. Its 5 distinct prime factors produce 288 positive divisors.

Prime Factor Structure

Factorization String 2^7 × 3 × 5^2 × 7^2 × 13

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 288

Divisor Sum (σ) 25,232,760

Proper Divisor Sum 19,117,560

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #6115199 ← → #6115229

Radix Representation

Decimal	6115200
Binary	10111010100111110000000 (23 bits)
Octal	0o27247600
Hexadecimal	0x5D4F80

Divisor Catalog (60 of 288)

1 2 3 4 5 6 7 8 10 12 13 14 15 16 20 21 24 25 26 28 30 32 35 39 40 42 48 49 50 52 56 60 64 65 70 75 78 80 84 91 96 98 100 104 105 112 120 128 130 140 147 150 156 160 168 175 182 192 195 196

Collatz Trajectory (108 steps to reach 1)

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

6,115,200 3,057,600 1,528,800 764,400 382,200 191,100 95,550 47,775 143,326 71,663 214,990 107,495 322,486 161,243 483,730 241,865 725,596 362,798 181,399 544,198 272,099 816,298 408,149 1,224,448 612,224 306,112 153,056 76,528 38,264 19,132 9,566 4,783 14,350 7,175 21,526 10,763 32,290 16,145 48,436 24,218 12,109 36,328 18,164 9,082 4,541 13,624 6,812 3,406 1,703 5,110 2,555 7,666 3,833 11,500 5,750 2,875 8,626 4,313 12,940 6,470

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