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Atlas › Integer Profiles › Node 9,971,990

9,971,990

2 × 5 × 72 × 47 × 433
Abundant Even Composite

9,971,990 factors as 2 × 5 × 7^2 × 47 × 433. Its 48 positive divisors give a proper-divisor sum of 11,401,642, so this integer is abundant. The Collatz stopping time is 189 steps.

Prime Factor Structure

Factorization String 2 × 5 × 7^2 × 47 × 433
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 21,373,632
Proper Divisor Sum 11,401,642
Digit Sum / Digital Root 44 (Root: 8)
Adjacent Primes #9971989 ← → #9971993

Radix Representation

Decimal 9971990
Binary 100110000010100100010110 (24 bits)
Octal 0o46024426
Hexadecimal 0x982916

Divisor Catalog (48)

1 2 5 7 10 14 35 47 49 70 94 98 235 245 329 433 470 490 658 866 1,645 2,165 2,303 3,031 3,290 4,330 4,606 6,062 11,515 15,155 20,351 21,217 23,030 30,310 40,702 42,434 101,755 106,085 142,457 203,510 212,170 284,914 712,285 997,199 1,424,570 1,994,398 4,985,995 9,971,990

Collatz Trajectory (189 steps to reach 1)

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

9,971,990 4,985,995 14,957,986 7,478,993 22,436,980 11,218,490 5,609,245 16,827,736 8,413,868 4,206,934 2,103,467 6,310,402 3,155,201 9,465,604 4,732,802 2,366,401 7,099,204 3,549,602 1,774,801 5,324,404 2,662,202 1,331,101 3,993,304 1,996,652 998,326 499,163 1,497,490 748,745 2,246,236 1,123,118 561,559 1,684,678 842,339 2,527,018 1,263,509 3,790,528 1,895,264 947,632 473,816 236,908 118,454 59,227 177,682 88,841 266,524 133,262 66,631 199,894 99,947 299,842 149,921 449,764 224,882 112,441 337,324 168,662 84,331 252,994 126,497 379,492

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