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684,540

22 × 32 × 5 × 3803
Abundant Even Composite

684,540 factors as 2^2 × 3^2 × 5 × 3803. Its 36 positive divisors give a proper-divisor sum of 1,392,444, so this integer is abundant. The Collatz stopping time is 136 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 5 × 3803
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 2,076,984
Proper Divisor Sum 1,392,444
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #684527 ← → #684547

Radix Representation

Decimal 684540
Binary 10100111000111111100 (20 bits)
Octal 0o2470774
Hexadecimal 0xA71FC

Divisor Catalog (36)

1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 60 90 180 3,803 7,606 11,409 15,212 19,015 22,818 34,227 38,030 45,636 57,045 68,454 76,060 114,090 136,908 171,135 228,180 342,270 684,540

Collatz Trajectory (136 steps to reach 1)

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

684,540 342,270 171,135 513,406 256,703 770,110 385,055 1,155,166 577,583 1,732,750 866,375 2,599,126 1,299,563 3,898,690 1,949,345 5,848,036 2,924,018 1,462,009 4,386,028 2,193,014 1,096,507 3,289,522 1,644,761 4,934,284 2,467,142 1,233,571 3,700,714 1,850,357 5,551,072 2,775,536 1,387,768 693,884 346,942 173,471 520,414 260,207 780,622 390,311 1,170,934 585,467 1,756,402 878,201 2,634,604 1,317,302 658,651 1,975,954 987,977 2,963,932 1,481,966 740,983 2,222,950 1,111,475 3,334,426 1,667,213 5,001,640 2,500,820 1,250,410 625,205 1,875,616 937,808

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