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Atlas › Integer Profiles › Node 15,768,200

15,768,200

23 × 52 × 72 × 1609
Abundant Even Composite

15,768,200 factors as 2^3 × 5^2 × 7^2 × 1609. Its 72 positive divisors give a proper-divisor sum of 26,904,850, so this integer is abundant. The Collatz stopping time is 368 steps.

Prime Factor Structure

Factorization String 2^3 × 5^2 × 7^2 × 1609
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 42,673,050
Proper Divisor Sum 26,904,850
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #15768191 ← → #15768209

Radix Representation

Decimal 15768200
Binary 111100001001101010001000 (24 bits)
Octal 0o74115210
Hexadecimal 0xF09A88

Divisor Catalog (60 of 72)

1 2 4 5 7 8 10 14 20 25 28 35 40 49 50 56 70 98 100 140 175 196 200 245 280 350 392 490 700 980 1,225 1,400 1,609 1,960 2,450 3,218 4,900 6,436 8,045 9,800 11,263 12,872 16,090 22,526 32,180 40,225 45,052 56,315 64,360 78,841 80,450 90,104 112,630 157,682 160,900 225,260 281,575 315,364 321,800 394,205

Collatz Trajectory (368 steps to reach 1)

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

15,768,200 7,884,100 3,942,050 1,971,025 5,913,076 2,956,538 1,478,269 4,434,808 2,217,404 1,108,702 554,351 1,663,054 831,527 2,494,582 1,247,291 3,741,874 1,870,937 5,612,812 2,806,406 1,403,203 4,209,610 2,104,805 6,314,416 3,157,208 1,578,604 789,302 394,651 1,183,954 591,977 1,775,932 887,966 443,983 1,331,950 665,975 1,997,926 998,963 2,996,890 1,498,445 4,495,336 2,247,668 1,123,834 561,917 1,685,752 842,876 421,438 210,719 632,158 316,079 948,238 474,119 1,422,358 711,179 2,133,538 1,066,769 3,200,308 1,600,154 800,077 2,400,232 1,200,116 600,058

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