7,725,200

2⁴ × 5² × 7 × 31 × 89

Starting at 7,725,200, the Collatz iteration reaches 1 after 124 steps. The first transition is 3862600; the starting value is even with 120 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 5^2 × 7 × 31 × 89

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 120

Divisor Sum (σ) 22,141,440

Proper Divisor Sum 14,416,240

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #7725199 ← → #7725239

Radix Representation

Decimal	7725200
Binary	11101011110000010010000 (23 bits)
Octal	0o35360220
Hexadecimal	0x75E090

Divisor Catalog (60 of 120)

1 2 4 5 7 8 10 14 16 20 25 28 31 35 40 50 56 62 70 80 89 100 112 124 140 155 175 178 200 217 248 280 310 350 356 400 434 445 496 560 620 623 700 712 775 868 890 1,085 1,240 1,246 1,400 1,424 1,550 1,736 1,780 2,170 2,225 2,480 2,492 2,759

Collatz Trajectory (124 steps to reach 1)

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

7,725,200 3,862,600 1,931,300 965,650 482,825 1,448,476 724,238 362,119 1,086,358 543,179 1,629,538 814,769 2,444,308 1,222,154 611,077 1,833,232 916,616 458,308 229,154 114,577 343,732 171,866 85,933 257,800 128,900 64,450 32,225 96,676 48,338 24,169 72,508 36,254 18,127 54,382 27,191 81,574 40,787 122,362 61,181 183,544 91,772 45,886 22,943 68,830 34,415 103,246 51,623 154,870 77,435 232,306 116,153 348,460 174,230 87,115 261,346 130,673 392,020 196,010 98,005 294,016

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