6,829,632

2⁶ × 3² × 71 × 167

6,829,632 has digital root 9. The neighboring primes are 6829619 and 6829637; its proper-divisor sum differs from the starting integer by 6,311,232.

Prime Factor Structure

Factorization String 2^6 × 3^2 × 71 × 167

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 84

Divisor Sum (σ) 19,970,496

Proper Divisor Sum 13,140,864

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #6829619 ← → #6829637

Radix Representation

Decimal	6829632
Binary	11010000011011001000000 (23 bits)
Octal	0o32033100
Hexadecimal	0x683640

Divisor Catalog (60 of 84)

1 2 3 4 6 8 9 12 16 18 24 32 36 48 64 71 72 96 142 144 167 192 213 284 288 334 426 501 568 576 639 668 852 1,002 1,136 1,278 1,336 1,503 1,704 2,004 2,272 2,556 2,672 3,006 3,408 4,008 4,544 5,112 5,344 6,012 6,816 8,016 10,224 10,688 11,857 12,024 13,632 16,032 20,448 23,714

Collatz Trajectory (77 steps to reach 1)

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

6,829,632 3,414,816 1,707,408 853,704 426,852 213,426 106,713 320,140 160,070 80,035 240,106 120,053 360,160 180,080 90,040 45,020 22,510 11,255 33,766 16,883 50,650 25,325 75,976 37,988 18,994 9,497 28,492 14,246 7,123 21,370 10,685 32,056 16,028 8,014 4,007 12,022 6,011 18,034 9,017 27,052 13,526 6,763 20,290 10,145 30,436 15,218 7,609 22,828 11,414 5,707 17,122 8,561 25,684 12,842 6,421 19,264 9,632 4,816 2,408 1,204

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