7,877,034

2 × 3³ × 11 × 89 × 149

Starting at 7,877,034, the Collatz iteration reaches 1 after 186 steps. The first transition is 3938517; the starting value is even with 64 positive divisors.

Prime Factor Structure

Factorization String 2 × 3^3 × 11 × 89 × 149

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 19,440,000

Proper Divisor Sum 11,562,966

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7876997 ← → #7877047

Radix Representation

Decimal	7877034
Binary	11110000011000110101010 (23 bits)
Octal	0o36030652
Hexadecimal	0x7831AA

Divisor Catalog (60 of 64)

1 2 3 6 9 11 18 22 27 33 54 66 89 99 149 178 198 267 297 298 447 534 594 801 894 979 1,341 1,602 1,639 1,958 2,403 2,682 2,937 3,278 4,023 4,806 4,917 5,874 8,046 8,811 9,834 13,261 14,751 17,622 26,433 26,522 29,502 39,783 44,253 52,866 79,566 88,506 119,349 145,871 238,698 291,742 358,047 437,613 716,094 875,226

Collatz Trajectory (186 steps to reach 1)

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

7,877,034 3,938,517 11,815,552 5,907,776 2,953,888 1,476,944 738,472 369,236 184,618 92,309 276,928 138,464 69,232 34,616 17,308 8,654 4,327 12,982 6,491 19,474 9,737 29,212 14,606 7,303 21,910 10,955 32,866 16,433 49,300 24,650 12,325 36,976 18,488 9,244 4,622 2,311 6,934 3,467 10,402 5,201 15,604 7,802 3,901 11,704 5,852 2,926 1,463 4,390 2,195 6,586 3,293 9,880 4,940 2,470 1,235 3,706 1,853 5,560 2,780 1,390

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