8,157,680

2⁴ × 5 × 107 × 953

Starting at 8,157,680, the Collatz iteration reaches 1 after 137 steps. The first transition is 4078840; the starting value is even with 40 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 5 × 107 × 953

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 40

Divisor Sum (σ) 19,163,952

Proper Divisor Sum 11,006,272

Digit Sum / Digital Root 35 (Root: 8)

Adjacent Primes #8157679 ← → #8157683

Radix Representation

Decimal	8157680
Binary	11111000111100111110000 (23 bits)
Octal	0o37074760
Hexadecimal	0x7C79F0

Divisor Catalog (40)

1 2 4 5 8 10 16 20 40 80 107 214 428 535 856 953 1,070 1,712 1,906 2,140 3,812 4,280 4,765 7,624 8,560 9,530 15,248 19,060 38,120 76,240 101,971 203,942 407,884 509,855 815,768 1,019,710 1,631,536 2,039,420 4,078,840 8,157,680

Collatz Trajectory (137 steps to reach 1)

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

8,157,680 4,078,840 2,039,420 1,019,710 509,855 1,529,566 764,783 2,294,350 1,147,175 3,441,526 1,720,763 5,162,290 2,581,145 7,743,436 3,871,718 1,935,859 5,807,578 2,903,789 8,711,368 4,355,684 2,177,842 1,088,921 3,266,764 1,633,382 816,691 2,450,074 1,225,037 3,675,112 1,837,556 918,778 459,389 1,378,168 689,084 344,542 172,271 516,814 258,407 775,222 387,611 1,162,834 581,417 1,744,252 872,126 436,063 1,308,190 654,095 1,962,286 981,143 2,943,430 1,471,715 4,415,146 2,207,573 6,622,720 3,311,360 1,655,680 827,840 413,920 206,960 103,480 51,740

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