7,780,864

2⁹ × 7 × 13 × 167

Starting at 7,780,864, the Collatz iteration reaches 1 after 80 steps. The first transition is 3890432; the starting value is even with 80 positive divisors.

Prime Factor Structure

Factorization String 2^9 × 7 × 13 × 167

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 19,248,768

Proper Divisor Sum 11,467,904

Digit Sum / Digital Root 40 (Root: 4)

Adjacent Primes #7780811 ← → #7780873

Radix Representation

Decimal	7780864
Binary	11101101011101000000000 (23 bits)
Octal	0o35535000
Hexadecimal	0x76BA00

Divisor Catalog (60 of 80)

1 2 4 7 8 13 14 16 26 28 32 52 56 64 91 104 112 128 167 182 208 224 256 334 364 416 448 512 668 728 832 896 1,169 1,336 1,456 1,664 1,792 2,171 2,338 2,672 2,912 3,328 3,584 4,342 4,676 5,344 5,824 6,656 8,684 9,352 10,688 11,648 15,197 17,368 18,704 21,376 23,296 30,394 34,736 37,408

Collatz Trajectory (80 steps to reach 1)

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

7,780,864 3,890,432 1,945,216 972,608 486,304 243,152 121,576 60,788 30,394 15,197 45,592 22,796 11,398 5,699 17,098 8,549 25,648 12,824 6,412 3,206 1,603 4,810 2,405 7,216 3,608 1,804 902 451 1,354 677 2,032 1,016 508 254 127 382 191 574 287 862 431 1,294 647 1,942 971 2,914 1,457 4,372 2,186 1,093 3,280 1,640 820 410 205 616 308 154 77 232

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