7,209,840

2⁴ × 3 × 5 × 11 × 2731

7,209,840 factors as 2^4 × 3 × 5 × 11 × 2731. Its 80 positive divisors give a proper-divisor sum of 17,181,456, so this integer is abundant. The Collatz stopping time is 235 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 5 × 11 × 2731

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 24,391,296

Proper Divisor Sum 17,181,456

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #7209827 ← → #7209841

Radix Representation

Decimal	7209840
Binary	11011100000001101110000 (23 bits)
Octal	0o33401560
Hexadecimal	0x6E0370

Divisor Catalog (60 of 80)

1 2 3 4 5 6 8 10 11 12 15 16 20 22 24 30 33 40 44 48 55 60 66 80 88 110 120 132 165 176 220 240 264 330 440 528 660 880 1,320 2,640 2,731 5,462 8,193 10,924 13,655 16,386 21,848 27,310 30,041 32,772 40,965 43,696 54,620 60,082 65,544 81,930 90,123 109,240 120,164 131,088

Collatz Trajectory (235 steps to reach 1)

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

7,209,840 3,604,920 1,802,460 901,230 450,615 1,351,846 675,923 2,027,770 1,013,885 3,041,656 1,520,828 760,414 380,207 1,140,622 570,311 1,710,934 855,467 2,566,402 1,283,201 3,849,604 1,924,802 962,401 2,887,204 1,443,602 721,801 2,165,404 1,082,702 541,351 1,624,054 812,027 2,436,082 1,218,041 3,654,124 1,827,062 913,531 2,740,594 1,370,297 4,110,892 2,055,446 1,027,723 3,083,170 1,541,585 4,624,756 2,312,378 1,156,189 3,468,568 1,734,284 867,142 433,571 1,300,714 650,357 1,951,072 975,536 487,768 243,884 121,942 60,971 182,914 91,457 274,372

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