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Atlas › Integer Profiles › Node 8,313,612

8,313,612

22 × 3 × 17 × 83 × 491
Abundant Even Composite

8,313,612 factors as 2^2 × 3 × 17 × 83 × 491. Its 48 positive divisors give a proper-divisor sum of 12,515,700, so this integer is abundant. The Collatz stopping time is 199 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 17 × 83 × 491
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 20,829,312
Proper Divisor Sum 12,515,700
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #8313589 ← → #8313619

Radix Representation

Decimal 8313612
Binary 11111101101101100001100 (23 bits)
Octal 0o37555414
Hexadecimal 0x7EDB0C

Divisor Catalog (48)

1 2 3 4 6 12 17 34 51 68 83 102 166 204 249 332 491 498 982 996 1,411 1,473 1,964 2,822 2,946 4,233 5,644 5,892 8,347 8,466 16,694 16,932 25,041 33,388 40,753 50,082 81,506 100,164 122,259 163,012 244,518 489,036 692,801 1,385,602 2,078,403 2,771,204 4,156,806 8,313,612

Collatz Trajectory (199 steps to reach 1)

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

8,313,612 4,156,806 2,078,403 6,235,210 3,117,605 9,352,816 4,676,408 2,338,204 1,169,102 584,551 1,753,654 876,827 2,630,482 1,315,241 3,945,724 1,972,862 986,431 2,959,294 1,479,647 4,438,942 2,219,471 6,658,414 3,329,207 9,987,622 4,993,811 14,981,434 7,490,717 22,472,152 11,236,076 5,618,038 2,809,019 8,427,058 4,213,529 12,640,588 6,320,294 3,160,147 9,480,442 4,740,221 14,220,664 7,110,332 3,555,166 1,777,583 5,332,750 2,666,375 7,999,126 3,999,563 11,998,690 5,999,345 17,998,036 8,999,018 4,499,509 13,498,528 6,749,264 3,374,632 1,687,316 843,658 421,829 1,265,488 632,744 316,372

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