8,309,628

2² × 3⁵ × 83 × 103

8,309,628 factors as 2^2 × 3^5 × 83 × 103. Its 72 positive divisors give a proper-divisor sum of 13,949,700, so this integer is abundant. The Collatz stopping time is 168 steps.

Prime Factor Structure

Factorization String 2^2 × 3^5 × 83 × 103

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 22,259,328

Proper Divisor Sum 13,949,700

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #8309611 ← → #8309629

Radix Representation

Decimal	8309628
Binary	11111101100101101111100 (23 bits)
Octal	0o37545574
Hexadecimal	0x7ECB7C

Divisor Catalog (60 of 72)

1 2 3 4 6 9 12 18 27 36 54 81 83 103 108 162 166 206 243 249 309 324 332 412 486 498 618 747 927 972 996 1,236 1,494 1,854 2,241 2,781 2,988 3,708 4,482 5,562 6,723 8,343 8,549 8,964 11,124 13,446 16,686 17,098 20,169 25,029 25,647 26,892 33,372 34,196 40,338 50,058 51,294 76,941 80,676 100,116

Collatz Trajectory (168 steps to reach 1)

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

8,309,628 4,154,814 2,077,407 6,232,222 3,116,111 9,348,334 4,674,167 14,022,502 7,011,251 21,033,754 10,516,877 31,550,632 15,775,316 7,887,658 3,943,829 11,831,488 5,915,744 2,957,872 1,478,936 739,468 369,734 184,867 554,602 277,301 831,904 415,952 207,976 103,988 51,994 25,997 77,992 38,996 19,498 9,749 29,248 14,624 7,312 3,656 1,828 914 457 1,372 686 343 1,030 515 1,546 773 2,320 1,160 580 290 145 436 218 109 328 164 82 41

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