6,345,840

2⁴ × 3 × 5 × 137 × 193

6,345,840 factors as 2^4 × 3 × 5 × 137 × 193. Its 80 positive divisors give a proper-divisor sum of 13,572,528, so this integer is abundant. The Collatz stopping time is 178 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 5 × 137 × 193

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 19,918,368

Proper Divisor Sum 13,572,528

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #6345839 ← → #6345851

Radix Representation

Decimal	6345840
Binary	11000001101010001110000 (23 bits)
Octal	0o30152160
Hexadecimal	0x60D470

Divisor Catalog (60 of 80)

1 2 3 4 5 6 8 10 12 15 16 20 24 30 40 48 60 80 120 137 193 240 274 386 411 548 579 685 772 822 965 1,096 1,158 1,370 1,544 1,644 1,930 2,055 2,192 2,316 2,740 2,895 3,088 3,288 3,860 4,110 4,632 5,480 5,790 6,576 7,720 8,220 9,264 10,960 11,580 15,440 16,440 23,160 26,441 32,880

Collatz Trajectory (178 steps to reach 1)

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

6,345,840 3,172,920 1,586,460 793,230 396,615 1,189,846 594,923 1,784,770 892,385 2,677,156 1,338,578 669,289 2,007,868 1,003,934 501,967 1,505,902 752,951 2,258,854 1,129,427 3,388,282 1,694,141 5,082,424 2,541,212 1,270,606 635,303 1,905,910 952,955 2,858,866 1,429,433 4,288,300 2,144,150 1,072,075 3,216,226 1,608,113 4,824,340 2,412,170 1,206,085 3,618,256 1,809,128 904,564 452,282 226,141 678,424 339,212 169,606 84,803 254,410 127,205 381,616 190,808 95,404 47,702 23,851 71,554 35,777 107,332 53,666 26,833 80,500 40,250

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