83,406,400

2⁶ × 5² × 7 × 11 × 677

83,406,400 factors as 2^6 × 5^2 × 7 × 11 × 677. Its 168 positive divisors give a proper-divisor sum of 172,845,056, so this integer is abundant. The Collatz stopping time is 192 steps.

Prime Factor Structure

Factorization String 2^6 × 5^2 × 7 × 11 × 677

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 168

Divisor Sum (σ) 256,251,456

Proper Divisor Sum 172,845,056

Digit Sum / Digital Root 25 (Root: 7)

Adjacent Primes #83406397 ← → #83406431

Radix Representation

Decimal	83406400
Binary	100111110001010111001000000 (27 bits)
Octal	0o476127100
Hexadecimal	0x4F8AE40

Divisor Catalog (60 of 168)

1 2 4 5 7 8 10 11 14 16 20 22 25 28 32 35 40 44 50 55 56 64 70 77 80 88 100 110 112 140 154 160 175 176 200 220 224 275 280 308 320 350 352 385 400 440 448 550 560 616 677 700 704 770 800 880 1,100 1,120 1,232 1,354

Collatz Trajectory (192 steps to reach 1)

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

83,406,400 41,703,200 20,851,600 10,425,800 5,212,900 2,606,450 1,303,225 3,909,676 1,954,838 977,419 2,932,258 1,466,129 4,398,388 2,199,194 1,099,597 3,298,792 1,649,396 824,698 412,349 1,237,048 618,524 309,262 154,631 463,894 231,947 695,842 347,921 1,043,764 521,882 260,941 782,824 391,412 195,706 97,853 293,560 146,780 73,390 36,695 110,086 55,043 165,130 82,565 247,696 123,848 61,924 30,962 15,481 46,444 23,222 11,611 34,834 17,417 52,252 26,126 13,063 39,190 19,595 58,786 29,393 88,180

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