7,905,800

2³ × 5² × 7 × 5647

Starting at 7,905,800, the Collatz iteration reaches 1 after 155 steps. The first transition is 3952900; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 5^2 × 7 × 5647

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 21,010,560

Proper Divisor Sum 13,104,760

Digit Sum / Digital Root 29 (Root: 2)

Adjacent Primes #7905797 ← → #7905803

Radix Representation

Decimal	7905800
Binary	11110001010001000001000 (23 bits)
Octal	0o36121010
Hexadecimal	0x78A208

Divisor Catalog (48)

1 2 4 5 7 8 10 14 20 25 28 35 40 50 56 70 100 140 175 200 280 350 700 1,400 5,647 11,294 22,588 28,235 39,529 45,176 56,470 79,058 112,940 141,175 158,116 197,645 225,880 282,350 316,232 395,290 564,700 790,580 988,225 1,129,400 1,581,160 1,976,450 3,952,900 7,905,800

Collatz Trajectory (155 steps to reach 1)

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

7,905,800 3,952,900 1,976,450 988,225 2,964,676 1,482,338 741,169 2,223,508 1,111,754 555,877 1,667,632 833,816 416,908 208,454 104,227 312,682 156,341 469,024 234,512 117,256 58,628 29,314 14,657 43,972 21,986 10,993 32,980 16,490 8,245 24,736 12,368 6,184 3,092 1,546 773 2,320 1,160 580 290 145 436 218 109 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242

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