7,725,848

2³ × 13 × 74287

Starting at 7,725,848, the Collatz iteration reaches 1 after 186 steps. The first transition is 3862924; the starting value is even with 16 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 13 × 74287

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 15,600,480

Proper Divisor Sum 7,874,632

Digit Sum / Digital Root 41 (Root: 5)

Adjacent Primes #7725821 ← → #7725857

Radix Representation

Decimal	7725848
Binary	11101011110001100011000 (23 bits)
Octal	0o35361430
Hexadecimal	0x75E318

Divisor Catalog (16)

1 2 4 8 13 26 52 104 74,287 148,574 297,148 594,296 965,731 1,931,462 3,862,924 7,725,848

Collatz Trajectory (186 steps to reach 1)

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

7,725,848 3,862,924 1,931,462 965,731 2,897,194 1,448,597 4,345,792 2,172,896 1,086,448 543,224 271,612 135,806 67,903 203,710 101,855 305,566 152,783 458,350 229,175 687,526 343,763 1,031,290 515,645 1,546,936 773,468 386,734 193,367 580,102 290,051 870,154 435,077 1,305,232 652,616 326,308 163,154 81,577 244,732 122,366 61,183 183,550 91,775 275,326 137,663 412,990 206,495 619,486 309,743 929,230 464,615 1,393,846 696,923 2,090,770 1,045,385 3,136,156 1,568,078 784,039 2,352,118 1,176,059 3,528,178 1,764,089

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