8,278,824

2³ × 3 × 37 × 9323

Starting at 8,278,824, the Collatz iteration reaches 1 after 137 steps. The first transition is 4139412; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3 × 37 × 9323

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 21,258,720

Proper Divisor Sum 12,979,896

Digit Sum / Digital Root 39 (Root: 3)

Adjacent Primes #8278817 ← → #8278841

Radix Representation

Decimal	8278824
Binary	11111100101001100101000 (23 bits)
Octal	0o37451450
Hexadecimal	0x7E5328

Divisor Catalog (32)

1 2 3 4 6 8 12 24 37 74 111 148 222 296 444 888 9,323 18,646 27,969 37,292 55,938 74,584 111,876 223,752 344,951 689,902 1,034,853 1,379,804 2,069,706 2,759,608 4,139,412 8,278,824

Collatz Trajectory (137 steps to reach 1)

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

8,278,824 4,139,412 2,069,706 1,034,853 3,104,560 1,552,280 776,140 388,070 194,035 582,106 291,053 873,160 436,580 218,290 109,145 327,436 163,718 81,859 245,578 122,789 368,368 184,184 92,092 46,046 23,023 69,070 34,535 103,606 51,803 155,410 77,705 233,116 116,558 58,279 174,838 87,419 262,258 131,129 393,388 196,694 98,347 295,042 147,521 442,564 221,282 110,641 331,924 165,962 82,981 248,944 124,472 62,236 31,118 15,559 46,678 23,339 70,018 35,009 105,028 52,514

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