7,664,540

2² × 5 × 13 × 41 × 719

Starting at 7,664,540, the Collatz iteration reaches 1 after 217 steps. The first transition is 3832270; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 5 × 13 × 41 × 719

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 17,781,120

Proper Divisor Sum 10,116,580

Digit Sum / Digital Root 32 (Root: 5)

Adjacent Primes #7664537 ← → #7664549

Radix Representation

Decimal	7664540
Binary	11101001111001110011100 (23 bits)
Octal	0o35171634
Hexadecimal	0x74F39C

Divisor Catalog (48)

1 2 4 5 10 13 20 26 41 52 65 82 130 164 205 260 410 533 719 820 1,066 1,438 2,132 2,665 2,876 3,595 5,330 7,190 9,347 10,660 14,380 18,694 29,479 37,388 46,735 58,958 93,470 117,916 147,395 186,940 294,790 383,227 589,580 766,454 1,532,908 1,916,135 3,832,270 7,664,540

Collatz Trajectory (217 steps to reach 1)

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

7,664,540 3,832,270 1,916,135 5,748,406 2,874,203 8,622,610 4,311,305 12,933,916 6,466,958 3,233,479 9,700,438 4,850,219 14,550,658 7,275,329 21,825,988 10,912,994 5,456,497 16,369,492 8,184,746 4,092,373 12,277,120 6,138,560 3,069,280 1,534,640 767,320 383,660 191,830 95,915 287,746 143,873 431,620 215,810 107,905 323,716 161,858 80,929 242,788 121,394 60,697 182,092 91,046 45,523 136,570 68,285 204,856 102,428 51,214 25,607 76,822 38,411 115,234 57,617 172,852 86,426 43,213 129,640 64,820 32,410 16,205 48,616

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