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Atlas › Integer Profiles › Node 9,712,944

9,712,944

24 × 32 × 37 × 1823
Abundant Even Composite

9,712,944 factors as 2^4 × 3^2 × 37 × 1823. Its 60 positive divisors give a proper-divisor sum of 18,219,792, so this integer is abundant. The Collatz stopping time is 194 steps.

Prime Factor Structure

Factorization String 2^4 × 3^2 × 37 × 1823
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 60
Divisor Sum (σ) 27,932,736
Proper Divisor Sum 18,219,792
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #9712931 ← → #9712949

Radix Representation

Decimal 9712944
Binary 100101000011010100110000 (24 bits)
Octal 0o45032460
Hexadecimal 0x943530

Divisor Catalog (60)

1 2 3 4 6 8 9 12 16 18 24 36 37 48 72 74 111 144 148 222 296 333 444 592 666 888 1,332 1,776 1,823 2,664 3,646 5,328 5,469 7,292 10,938 14,584 16,407 21,876 29,168 32,814 43,752 65,628 67,451 87,504 131,256 134,902 202,353 262,512 269,804 404,706 539,608 607,059 809,412 1,079,216 1,214,118 1,618,824 2,428,236 3,237,648 4,856,472 9,712,944

Collatz Trajectory (194 steps to reach 1)

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

9,712,944 4,856,472 2,428,236 1,214,118 607,059 1,821,178 910,589 2,731,768 1,365,884 682,942 341,471 1,024,414 512,207 1,536,622 768,311 2,304,934 1,152,467 3,457,402 1,728,701 5,186,104 2,593,052 1,296,526 648,263 1,944,790 972,395 2,917,186 1,458,593 4,375,780 2,187,890 1,093,945 3,281,836 1,640,918 820,459 2,461,378 1,230,689 3,692,068 1,846,034 923,017 2,769,052 1,384,526 692,263 2,076,790 1,038,395 3,115,186 1,557,593 4,672,780 2,336,390 1,168,195 3,504,586 1,752,293 5,256,880 2,628,440 1,314,220 657,110 328,555 985,666 492,833 1,478,500 739,250 369,625

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