λ
Ratio Atlas
Atlas › Integer Profiles › Node 84,045,640

84,045,640

23 × 5 × 7 × 300163
Abundant Even Composite

84,045,640 factors as 2^3 × 5 × 7 × 300163. Its 32 positive divisors give a proper-divisor sum of 132,072,440, so this integer is abundant. The Collatz stopping time is 205 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 7 × 300163
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 216,118,080
Proper Divisor Sum 132,072,440
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #84045581 ← → #84045641

Radix Representation

Decimal 84045640
Binary 101000000100110111101001000 (27 bits)
Octal 0o500467510
Hexadecimal 0x5026F48

Divisor Catalog (32)

1 2 4 5 7 8 10 14 20 28 35 40 56 70 140 280 300,163 600,326 1,200,652 1,500,815 2,101,141 2,401,304 3,001,630 4,202,282 6,003,260 8,404,564 10,505,705 12,006,520 16,809,128 21,011,410 42,022,820 84,045,640

Collatz Trajectory (205 steps to reach 1)

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

84,045,640 42,022,820 21,011,410 10,505,705 31,517,116 15,758,558 7,879,279 23,637,838 11,818,919 35,456,758 17,728,379 53,185,138 26,592,569 79,777,708 39,888,854 19,944,427 59,833,282 29,916,641 89,749,924 44,874,962 22,437,481 67,312,444 33,656,222 16,828,111 50,484,334 25,242,167 75,726,502 37,863,251 113,589,754 56,794,877 170,384,632 85,192,316 42,596,158 21,298,079 63,894,238 31,947,119 95,841,358 47,920,679 143,762,038 71,881,019 215,643,058 107,821,529 323,464,588 161,732,294 80,866,147 242,598,442 121,299,221 363,897,664 181,948,832 90,974,416 45,487,208 22,743,604 11,371,802 5,685,901 17,057,704 8,528,852 4,264,426 2,132,213 6,396,640 3,198,320

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