7,829,280

2⁵ × 3² × 5 × 5437

7,829,280 has the prime decomposition 2^5 × 3^2 × 5 × 5437. Its 4 distinct prime factors produce 72 positive divisors.

Prime Factor Structure

Factorization String 2^5 × 3^2 × 5 × 5437

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 26,722,332

Proper Divisor Sum 18,893,052

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7829251 ← → #7829291

Radix Representation

Decimal	7829280
Binary	11101110111011100100000 (23 bits)
Octal	0o35673440
Hexadecimal	0x777720

Divisor Catalog (60 of 72)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 32 36 40 45 48 60 72 80 90 96 120 144 160 180 240 288 360 480 720 1,440 5,437 10,874 16,311 21,748 27,185 32,622 43,496 48,933 54,370 65,244 81,555 86,992 97,866 108,740 130,488 163,110 173,984 195,732 217,480 244,665 260,976 326,220 391,464 434,960

Collatz Trajectory (93 steps to reach 1)

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

7,829,280 3,914,640 1,957,320 978,660 489,330 244,665 733,996 366,998 183,499 550,498 275,249 825,748 412,874 206,437 619,312 309,656 154,828 77,414 38,707 116,122 58,061 174,184 87,092 43,546 21,773 65,320 32,660 16,330 8,165 24,496 12,248 6,124 3,062 1,531 4,594 2,297 6,892 3,446 1,723 5,170 2,585 7,756 3,878 1,939 5,818 2,909 8,728 4,364 2,182 1,091 3,274 1,637 4,912 2,456 1,228 614 307 922 461 1,384

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