7,946,250

2 × 3 × 5⁴ × 13 × 163

Starting at 7,946,250, the Collatz iteration reaches 1 after 129 steps. The first transition is 3973125; the starting value is even with 80 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 5^4 × 13 × 163

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 21,518,112

Proper Divisor Sum 13,571,862

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #7946233 ← → #7946303

Radix Representation

Decimal	7946250
Binary	11110010100000000001010 (23 bits)
Octal	0o36240012
Hexadecimal	0x79400A

Divisor Catalog (60 of 80)

1 2 3 5 6 10 13 15 25 26 30 39 50 65 75 78 125 130 150 163 195 250 325 326 375 390 489 625 650 750 815 975 978 1,250 1,625 1,630 1,875 1,950 2,119 2,445 3,250 3,750 4,075 4,238 4,875 4,890 6,357 8,125 8,150 9,750 10,595 12,225 12,714 16,250 20,375 21,190 24,375 24,450 31,785 40,750

Collatz Trajectory (129 steps to reach 1)

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

7,946,250 3,973,125 11,919,376 5,959,688 2,979,844 1,489,922 744,961 2,234,884 1,117,442 558,721 1,676,164 838,082 419,041 1,257,124 628,562 314,281 942,844 471,422 235,711 707,134 353,567 1,060,702 530,351 1,591,054 795,527 2,386,582 1,193,291 3,579,874 1,789,937 5,369,812 2,684,906 1,342,453 4,027,360 2,013,680 1,006,840 503,420 251,710 125,855 377,566 188,783 566,350 283,175 849,526 424,763 1,274,290 637,145 1,911,436 955,718 477,859 1,433,578 716,789 2,150,368 1,075,184 537,592 268,796 134,398 67,199 201,598 100,799 302,398

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