7,821,709

7 × 617 × 1811

Starting at 7,821,709, the Collatz iteration reaches 1 after 186 steps. The first transition is 23465128; the starting value is odd with 8 positive divisors.

Prime Factor Structure

Factorization String 7 × 617 × 1811

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 8,958,528

Proper Divisor Sum 1,136,819

Digit Sum / Digital Root 34 (Root: 7)

Adjacent Primes #7821701 ← → #7821719

Radix Representation

Decimal	7821709
Binary	11101110101100110001101 (23 bits)
Octal	0o35654615
Hexadecimal	0x77598D

Divisor Catalog (8)

1 7 617 1,811 4,319 12,677 1,117,387 7,821,709

Collatz Trajectory (186 steps to reach 1)

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

7,821,709 23,465,128 11,732,564 5,866,282 2,933,141 8,799,424 4,399,712 2,199,856 1,099,928 549,964 274,982 137,491 412,474 206,237 618,712 309,356 154,678 77,339 232,018 116,009 348,028 174,014 87,007 261,022 130,511 391,534 195,767 587,302 293,651 880,954 440,477 1,321,432 660,716 330,358 165,179 495,538 247,769 743,308 371,654 185,827 557,482 278,741 836,224 418,112 209,056 104,528 52,264 26,132 13,066 6,533 19,600 9,800 4,900 2,450 1,225 3,676 1,838 919 2,758 1,379

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