785,813

7³ × 29 × 79

Starting at 785,813, the Collatz iteration reaches 1 after 56 steps. The first transition is 2357440; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 7^3 × 29 × 79

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 960,000

Proper Divisor Sum 174,187

Digit Sum / Digital Root 32 (Root: 5)

Adjacent Primes #785809 ← → #785839

Radix Representation

Decimal	785813
Binary	10111111110110010101 (20 bits)
Octal	0o2776625
Hexadecimal	0xBFD95

Divisor Catalog (16)

1 7 29 49 79 203 343 553 1,421 2,291 3,871 9,947 16,037 27,097 112,259 785,813

Collatz Trajectory (56 steps to reach 1)

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

785,813 2,357,440 1,178,720 589,360 294,680 147,340 73,670 36,835 110,506 55,253 165,760 82,880 41,440 20,720 10,360 5,180 2,590 1,295 3,886 1,943 5,830 2,915 8,746 4,373 13,120 6,560 3,280 1,640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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