7,912,800

2⁵ × 3² × 5² × 7 × 157

Starting at 7,912,800, the Collatz iteration reaches 1 after 173 steps. The first transition is 3956400; the starting value is even with 216 positive divisors.

Prime Factor Structure

Factorization String 2^5 × 3^2 × 5^2 × 7 × 157

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 216

Divisor Sum (σ) 32,091,696

Proper Divisor Sum 24,178,896

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #7912787 ← → #7912811

Radix Representation

Decimal	7912800
Binary	11110001011110101100000 (23 bits)
Octal	0o36136540
Hexadecimal	0x78BD60

Divisor Catalog (60 of 216)

1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 28 30 32 35 36 40 42 45 48 50 56 60 63 70 72 75 80 84 90 96 100 105 112 120 126 140 144 150 157 160 168 175 180 200 210 224 225 240 252 280 288

Collatz Trajectory (173 steps to reach 1)

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

7,912,800 3,956,400 1,978,200 989,100 494,550 247,275 741,826 370,913 1,112,740 556,370 278,185 834,556 417,278 208,639 625,918 312,959 938,878 469,439 1,408,318 704,159 2,112,478 1,056,239 3,168,718 1,584,359 4,753,078 2,376,539 7,129,618 3,564,809 10,694,428 5,347,214 2,673,607 8,020,822 4,010,411 12,031,234 6,015,617 18,046,852 9,023,426 4,511,713 13,535,140 6,767,570 3,383,785 10,151,356 5,075,678 2,537,839 7,613,518 3,806,759 11,420,278 5,710,139 17,130,418 8,565,209 25,695,628 12,847,814 6,423,907 19,271,722 9,635,861 28,907,584 14,453,792 7,226,896 3,613,448 1,806,724

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