7,702,020

2² × 3³ × 5 × 17 × 839

7,702,020 factors as 2^2 × 3^3 × 5 × 17 × 839. Its 96 positive divisors give a proper-divisor sum of 17,699,580, so this integer is abundant. The Collatz stopping time is 111 steps.

Prime Factor Structure

Factorization String 2^2 × 3^3 × 5 × 17 × 839

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 25,401,600

Proper Divisor Sum 17,699,580

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #7702001 ← → #7702063

Radix Representation

Decimal	7702020
Binary	11101011000011000000100 (23 bits)
Octal	0o35303004
Hexadecimal	0x758604

Divisor Catalog (60 of 96)

1 2 3 4 5 6 9 10 12 15 17 18 20 27 30 34 36 45 51 54 60 68 85 90 102 108 135 153 170 180 204 255 270 306 340 459 510 540 612 765 839 918 1,020 1,530 1,678 1,836 2,295 2,517 3,060 3,356 4,195 4,590 5,034 7,551 8,390 9,180 10,068 12,585 14,263 15,102

Collatz Trajectory (111 steps to reach 1)

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

7,702,020 3,851,010 1,925,505 5,776,516 2,888,258 1,444,129 4,332,388 2,166,194 1,083,097 3,249,292 1,624,646 812,323 2,436,970 1,218,485 3,655,456 1,827,728 913,864 456,932 228,466 114,233 342,700 171,350 85,675 257,026 128,513 385,540 192,770 96,385 289,156 144,578 72,289 216,868 108,434 54,217 162,652 81,326 40,663 121,990 60,995 182,986 91,493 274,480 137,240 68,620 34,310 17,155 51,466 25,733 77,200 38,600 19,300 9,650 4,825 14,476 7,238 3,619 10,858 5,429 16,288 8,144

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