6,640,725

3 × 5² × 7² × 13 × 139

Starting at 6,640,725, the Collatz iteration reaches 1 after 103 steps. The first transition is 19922176; the starting value is odd with 72 positive divisors.

Prime Factor Structure

Factorization String 3 × 5^2 × 7^2 × 13 × 139

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 13,853,280

Proper Divisor Sum 7,212,555

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #6640687 ← → #6640757

Radix Representation

Decimal	6640725
Binary	11001010101010001010101 (23 bits)
Octal	0o31252125
Hexadecimal	0x655455

Divisor Catalog (60 of 72)

1 3 5 7 13 15 21 25 35 39 49 65 75 91 105 139 147 175 195 245 273 325 417 455 525 637 695 735 973 975 1,225 1,365 1,807 1,911 2,085 2,275 2,919 3,185 3,475 3,675 4,865 5,421 6,811 6,825 9,035 9,555 10,425 12,649 14,595 15,925 20,433 24,325 27,105 34,055 37,947 45,175 47,775 63,245 72,975 88,543

Collatz Trajectory (103 steps to reach 1)

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

6,640,725 19,922,176 9,961,088 4,980,544 2,490,272 1,245,136 622,568 311,284 155,642 77,821 233,464 116,732 58,366 29,183 87,550 43,775 131,326 65,663 196,990 98,495 295,486 147,743 443,230 221,615 664,846 332,423 997,270 498,635 1,495,906 747,953 2,243,860 1,121,930 560,965 1,682,896 841,448 420,724 210,362 105,181 315,544 157,772 78,886 39,443 118,330 59,165 177,496 88,748 44,374 22,187 66,562 33,281 99,844 49,922 24,961 74,884 37,442 18,721 56,164 28,082 14,041 42,124

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