7,717,860

2² × 3² × 5 × 53 × 809

7,717,860 factors as 2^2 × 3^2 × 5 × 53 × 809. Its 72 positive divisors give a proper-divisor sum of 16,164,180, so this integer is abundant. The Collatz stopping time is 230 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 5 × 53 × 809

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 23,882,040

Proper Divisor Sum 16,164,180

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7717859 ← → #7717873

Radix Representation

Decimal	7717860
Binary	11101011100001111100100 (23 bits)
Octal	0o35341744
Hexadecimal	0x75C3E4

Divisor Catalog (60 of 72)

1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 53 60 90 106 159 180 212 265 318 477 530 636 795 809 954 1,060 1,590 1,618 1,908 2,385 2,427 3,180 3,236 4,045 4,770 4,854 7,281 8,090 9,540 9,708 12,135 14,562 16,180 24,270 29,124 36,405 42,877 48,540 72,810 85,754 128,631 145,620 171,508 214,385 257,262

Collatz Trajectory (230 steps to reach 1)

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

7,717,860 3,858,930 1,929,465 5,788,396 2,894,198 1,447,099 4,341,298 2,170,649 6,511,948 3,255,974 1,627,987 4,883,962 2,441,981 7,325,944 3,662,972 1,831,486 915,743 2,747,230 1,373,615 4,120,846 2,060,423 6,181,270 3,090,635 9,271,906 4,635,953 13,907,860 6,953,930 3,476,965 10,430,896 5,215,448 2,607,724 1,303,862 651,931 1,955,794 977,897 2,933,692 1,466,846 733,423 2,200,270 1,100,135 3,300,406 1,650,203 4,950,610 2,475,305 7,425,916 3,712,958 1,856,479 5,569,438 2,784,719 8,354,158 4,177,079 12,531,238 6,265,619 18,796,858 9,398,429 28,195,288 14,097,644 7,048,822 3,524,411 10,573,234

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