6,516,760

2³ × 5 × 197 × 827

Starting at 6,516,760, the Collatz iteration reaches 1 after 90 steps. The first transition is 3258380; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 5 × 197 × 827

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 14,754,960

Proper Divisor Sum 8,238,200

Digit Sum / Digital Root 31 (Root: 4)

Adjacent Primes #6516743 ← → #6516761

Radix Representation

Decimal	6516760
Binary	11000110111000000011000 (23 bits)
Octal	0o30670030
Hexadecimal	0x637018

Divisor Catalog (32)

1 2 4 5 8 10 20 40 197 394 788 827 985 1,576 1,654 1,970 3,308 3,940 4,135 6,616 7,880 8,270 16,540 33,080 162,919 325,838 651,676 814,595 1,303,352 1,629,190 3,258,380 6,516,760

Collatz Trajectory (90 steps to reach 1)

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

6,516,760 3,258,380 1,629,190 814,595 2,443,786 1,221,893 3,665,680 1,832,840 916,420 458,210 229,105 687,316 343,658 171,829 515,488 257,744 128,872 64,436 32,218 16,109 48,328 24,164 12,082 6,041 18,124 9,062 4,531 13,594 6,797 20,392 10,196 5,098 2,549 7,648 3,824 1,912 956 478 239 718 359 1,078 539 1,618 809 2,428 1,214 607 1,822 911 2,734 1,367 4,102 2,051 6,154 3,077 9,232 4,616 2,308 1,154

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