8,109,972

2² × 3² × 13² × 31 × 43

8,109,972 factors as 2^2 × 3^2 × 13^2 × 31 × 43. Its 108 positive divisors give a proper-divisor sum of 15,337,452, so this integer is abundant. The Collatz stopping time is 248 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 13^2 × 31 × 43

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 108

Divisor Sum (σ) 23,447,424

Proper Divisor Sum 15,337,452

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #8109971 ← → #8109973

Radix Representation

Decimal	8109972
Binary	11110111011111110010100 (23 bits)
Octal	0o36737624
Hexadecimal	0x7BBF94

Divisor Catalog (60 of 108)

1 2 3 4 6 9 12 13 18 26 31 36 39 43 52 62 78 86 93 117 124 129 156 169 172 186 234 258 279 338 372 387 403 468 507 516 558 559 676 774 806 1,014 1,116 1,118 1,209 1,333 1,521 1,548 1,612 1,677 2,028 2,236 2,418 2,666 3,042 3,354 3,627 3,999 4,836 5,031

Collatz Trajectory (248 steps to reach 1)

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

8,109,972 4,054,986 2,027,493 6,082,480 3,041,240 1,520,620 760,310 380,155 1,140,466 570,233 1,710,700 855,350 427,675 1,283,026 641,513 1,924,540 962,270 481,135 1,443,406 721,703 2,165,110 1,082,555 3,247,666 1,623,833 4,871,500 2,435,750 1,217,875 3,653,626 1,826,813 5,480,440 2,740,220 1,370,110 685,055 2,055,166 1,027,583 3,082,750 1,541,375 4,624,126 2,312,063 6,936,190 3,468,095 10,404,286 5,202,143 15,606,430 7,803,215 23,409,646 11,704,823 35,114,470 17,557,235 52,671,706 26,335,853 79,007,560 39,503,780 19,751,890 9,875,945 29,627,836 14,813,918 7,406,959 22,220,878 11,110,439

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