7,688,835

3² × 5 × 7² × 11 × 317

7,688,835 has the prime decomposition 3^2 × 5 × 7^2 × 11 × 317. Its 5 distinct prime factors produce 72 positive divisors.

Prime Factor Structure

Factorization String 3^2 × 5 × 7^2 × 11 × 317

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 16,965,936

Proper Divisor Sum 9,277,101

Digit Sum / Digital Root 45 (Root: 9)

Adjacent Primes #7688809 ← → #7688839

Radix Representation

Decimal	7688835
Binary	11101010101001010000011 (23 bits)
Octal	0o35251203
Hexadecimal	0x755283

Divisor Catalog (60 of 72)

1 3 5 7 9 11 15 21 33 35 45 49 55 63 77 99 105 147 165 231 245 315 317 385 441 495 539 693 735 951 1,155 1,585 1,617 2,205 2,219 2,695 2,853 3,465 3,487 4,755 4,851 6,657 8,085 10,461 11,095 14,265 15,533 17,435 19,971 24,255 24,409 31,383 33,285 46,599 52,305 73,227 77,665 99,855 122,045 139,797

Collatz Trajectory (173 steps to reach 1)

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

7,688,835 23,066,506 11,533,253 34,599,760 17,299,880 8,649,940 4,324,970 2,162,485 6,487,456 3,243,728 1,621,864 810,932 405,466 202,733 608,200 304,100 152,050 76,025 228,076 114,038 57,019 171,058 85,529 256,588 128,294 64,147 192,442 96,221 288,664 144,332 72,166 36,083 108,250 54,125 162,376 81,188 40,594 20,297 60,892 30,446 15,223 45,670 22,835 68,506 34,253 102,760 51,380 25,690 12,845 38,536 19,268 9,634 4,817 14,452 7,226 3,613 10,840 5,420 2,710 1,355

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