7,822,960

2⁴ × 5 × 97787

Starting at 7,822,960, the Collatz iteration reaches 1 after 98 steps. The first transition is 3911480; the starting value is even with 20 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 5 × 97787

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 20

Divisor Sum (σ) 18,188,568

Proper Divisor Sum 10,365,608

Digit Sum / Digital Root 34 (Root: 7)

Adjacent Primes #7822951 ← → #7822961

Radix Representation

Decimal	7822960
Binary	11101110101111001110000 (23 bits)
Octal	0o35657160
Hexadecimal	0x775E70

Divisor Catalog (20)

1 2 4 5 8 10 16 20 40 80 97,787 195,574 391,148 488,935 782,296 977,870 1,564,592 1,955,740 3,911,480 7,822,960

Collatz Trajectory (98 steps to reach 1)

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

7,822,960 3,911,480 1,955,740 977,870 488,935 1,466,806 733,403 2,200,210 1,100,105 3,300,316 1,650,158 825,079 2,475,238 1,237,619 3,712,858 1,856,429 5,569,288 2,784,644 1,392,322 696,161 2,088,484 1,044,242 522,121 1,566,364 783,182 391,591 1,174,774 587,387 1,762,162 881,081 2,643,244 1,321,622 660,811 1,982,434 991,217 2,973,652 1,486,826 743,413 2,230,240 1,115,120 557,560 278,780 139,390 69,695 209,086 104,543 313,630 156,815 470,446 235,223 705,670 352,835 1,058,506 529,253 1,587,760 793,880 396,940 198,470 99,235 297,706

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