7,827,218

2 × 7 × 523 × 1069

Starting at 7,827,218, the Collatz iteration reaches 1 after 217 steps. The first transition is 3913609; the starting value is even with 16 positive divisors.

Prime Factor Structure

Factorization String 2 × 7 × 523 × 1069

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 13,456,320

Proper Divisor Sum 5,629,102

Digit Sum / Digital Root 35 (Root: 8)

Adjacent Primes #7827217 ← → #7827223

Radix Representation

Decimal	7827218
Binary	11101110110111100010010 (23 bits)
Octal	0o35667422
Hexadecimal	0x776F12

Divisor Catalog (16)

1 2 7 14 523 1,046 1,069 2,138 3,661 7,322 7,483 14,966 559,087 1,118,174 3,913,609 7,827,218

Collatz Trajectory (217 steps to reach 1)

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

7,827,218 3,913,609 11,740,828 5,870,414 2,935,207 8,805,622 4,402,811 13,208,434 6,604,217 19,812,652 9,906,326 4,953,163 14,859,490 7,429,745 22,289,236 11,144,618 5,572,309 16,716,928 8,358,464 4,179,232 2,089,616 1,044,808 522,404 261,202 130,601 391,804 195,902 97,951 293,854 146,927 440,782 220,391 661,174 330,587 991,762 495,881 1,487,644 743,822 371,911 1,115,734 557,867 1,673,602 836,801 2,510,404 1,255,202 627,601 1,882,804 941,402 470,701 1,412,104 706,052 353,026 176,513 529,540 264,770 132,385 397,156 198,578 99,289 297,868

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