8,729,580

2² × 3 × 5 × 29² × 173

Starting at 8,729,580, the Collatz iteration reaches 1 after 274 steps. The first transition is 4364790; the starting value is even with 72 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 29^2 × 173

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 25,461,072

Proper Divisor Sum 16,731,492

Digit Sum / Digital Root 39 (Root: 3)

Adjacent Primes #8729563 ← → #8729593

Radix Representation

Decimal	8729580
Binary	100001010011001111101100 (24 bits)
Octal	0o41231754
Hexadecimal	0x8533EC

Divisor Catalog (60 of 72)

1 2 3 4 5 6 10 12 15 20 29 30 58 60 87 116 145 173 174 290 346 348 435 519 580 692 841 865 870 1,038 1,682 1,730 1,740 2,076 2,523 2,595 3,364 3,460 4,205 5,017 5,046 5,190 8,410 10,034 10,092 10,380 12,615 15,051 16,820 20,068 25,085 25,230 30,102 50,170 50,460 60,204 75,255 100,340 145,493 150,510

Collatz Trajectory (274 steps to reach 1)

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

8,729,580 4,364,790 2,182,395 6,547,186 3,273,593 9,820,780 4,910,390 2,455,195 7,365,586 3,682,793 11,048,380 5,524,190 2,762,095 8,286,286 4,143,143 12,429,430 6,214,715 18,644,146 9,322,073 27,966,220 13,983,110 6,991,555 20,974,666 10,487,333 31,462,000 15,731,000 7,865,500 3,932,750 1,966,375 5,899,126 2,949,563 8,848,690 4,424,345 13,273,036 6,636,518 3,318,259 9,954,778 4,977,389 14,932,168 7,466,084 3,733,042 1,866,521 5,599,564 2,799,782 1,399,891 4,199,674 2,099,837 6,299,512 3,149,756 1,574,878 787,439 2,362,318 1,181,159 3,543,478 1,771,739 5,315,218 2,657,609 7,972,828 3,986,414 1,993,207

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