6,857,210

2 × 5 × 37 × 43 × 431

Starting at 6,857,210, the Collatz iteration reaches 1 after 129 steps. The first transition is 3428605; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2 × 5 × 37 × 43 × 431

Distinct Prime Factors 5

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 13,001,472

Proper Divisor Sum 6,144,262

Digit Sum / Digital Root 29 (Root: 2)

Adjacent Primes #6857203 ← → #6857219

Radix Representation

Decimal	6857210
Binary	11010001010000111111010 (23 bits)
Octal	0o32120772
Hexadecimal	0x68A1FA

Divisor Catalog (32)

1 2 5 10 37 43 74 86 185 215 370 430 431 862 1,591 2,155 3,182 4,310 7,955 15,910 15,947 18,533 31,894 37,066 79,735 92,665 159,470 185,330 685,721 1,371,442 3,428,605 6,857,210

Collatz Trajectory (129 steps to reach 1)

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

6,857,210 3,428,605 10,285,816 5,142,908 2,571,454 1,285,727 3,857,182 1,928,591 5,785,774 2,892,887 8,678,662 4,339,331 13,017,994 6,508,997 19,526,992 9,763,496 4,881,748 2,440,874 1,220,437 3,661,312 1,830,656 915,328 457,664 228,832 114,416 57,208 28,604 14,302 7,151 21,454 10,727 32,182 16,091 48,274 24,137 72,412 36,206 18,103 54,310 27,155 81,466 40,733 122,200 61,100 30,550 15,275 45,826 22,913 68,740 34,370 17,185 51,556 25,778 12,889 38,668 19,334 9,667 29,002 14,501 43,504

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