λ
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Atlas › Integer Profiles › Node 82,342,480

82,342,480

24 × 5 × 11 × 137 × 683
Abundant Even Composite

82,342,480 factors as 2^4 × 5 × 11 × 137 × 683. Its 80 positive divisors give a proper-divisor sum of 128,340,464, so this integer is abundant. The Collatz stopping time is 130 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 11 × 137 × 683
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 210,682,944
Proper Divisor Sum 128,340,464
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #82342471 ← → #82342489

Radix Representation

Decimal 82342480
Binary 100111010000111001001010000 (27 bits)
Octal 0o472071120
Hexadecimal 0x4E87250

Divisor Catalog (60 of 80)

1 2 4 5 8 10 11 16 20 22 40 44 55 80 88 110 137 176 220 274 440 548 683 685 880 1,096 1,366 1,370 1,507 2,192 2,732 2,740 3,014 3,415 5,464 5,480 6,028 6,830 7,513 7,535 10,928 10,960 12,056 13,660 15,026 15,070 24,112 27,320 30,052 30,140 37,565 54,640 60,104 60,280 75,130 93,571 120,208 120,560 150,260 187,142

Collatz Trajectory (130 steps to reach 1)

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

82,342,480 41,171,240 20,585,620 10,292,810 5,146,405 15,439,216 7,719,608 3,859,804 1,929,902 964,951 2,894,854 1,447,427 4,342,282 2,171,141 6,513,424 3,256,712 1,628,356 814,178 407,089 1,221,268 610,634 305,317 915,952 457,976 228,988 114,494 57,247 171,742 85,871 257,614 128,807 386,422 193,211 579,634 289,817 869,452 434,726 217,363 652,090 326,045 978,136 489,068 244,534 122,267 366,802 183,401 550,204 275,102 137,551 412,654 206,327 618,982 309,491 928,474 464,237 1,392,712 696,356 348,178 174,089 522,268

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