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Atlas › Integer Profiles › Node 9,735,540

9,735,540

22 × 3 × 5 × 211 × 769
Abundant Even Composite

9,735,540 factors as 2^2 × 3 × 5 × 211 × 769. Its 48 positive divisors give a proper-divisor sum of 17,688,780, so this integer is abundant. The Collatz stopping time is 163 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 211 × 769
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 27,424,320
Proper Divisor Sum 17,688,780
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #9735521 ← → #9735541

Radix Representation

Decimal 9735540
Binary 100101001000110101110100 (24 bits)
Octal 0o45106564
Hexadecimal 0x948D74

Divisor Catalog (48)

1 2 3 4 5 6 10 12 15 20 30 60 211 422 633 769 844 1,055 1,266 1,538 2,110 2,307 2,532 3,076 3,165 3,845 4,220 4,614 6,330 7,690 9,228 11,535 12,660 15,380 23,070 46,140 162,259 324,518 486,777 649,036 811,295 973,554 1,622,590 1,947,108 2,433,885 3,245,180 4,867,770 9,735,540

Collatz Trajectory (163 steps to reach 1)

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

9,735,540 4,867,770 2,433,885 7,301,656 3,650,828 1,825,414 912,707 2,738,122 1,369,061 4,107,184 2,053,592 1,026,796 513,398 256,699 770,098 385,049 1,155,148 577,574 288,787 866,362 433,181 1,299,544 649,772 324,886 162,443 487,330 243,665 730,996 365,498 182,749 548,248 274,124 137,062 68,531 205,594 102,797 308,392 154,196 77,098 38,549 115,648 57,824 28,912 14,456 7,228 3,614 1,807 5,422 2,711 8,134 4,067 12,202 6,101 18,304 9,152 4,576 2,288 1,144 572 286

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