7,731,828

2² × 3³ × 13 × 5507

7,731,828 is even and not a perfect square. Its factorization is 2^2 × 3^3 × 13 × 5507 and its 48 divisors sum to 21,591,360.

Prime Factor Structure

Factorization String 2^2 × 3^3 × 13 × 5507

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 21,591,360

Proper Divisor Sum 13,859,532

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7731827 ← → #7731839

Radix Representation

Decimal	7731828
Binary	11101011111101001110100 (23 bits)
Octal	0o35375164
Hexadecimal	0x75FA74

Divisor Catalog (48)

1 2 3 4 6 9 12 13 18 26 27 36 39 52 54 78 108 117 156 234 351 468 702 1,404 5,507 11,014 16,521 22,028 33,042 49,563 66,084 71,591 99,126 143,182 148,689 198,252 214,773 286,364 297,378 429,546 594,756 644,319 859,092 1,288,638 1,932,957 2,577,276 3,865,914 7,731,828

Collatz Trajectory (124 steps to reach 1)

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

7,731,828 3,865,914 1,932,957 5,798,872 2,899,436 1,449,718 724,859 2,174,578 1,087,289 3,261,868 1,630,934 815,467 2,446,402 1,223,201 3,669,604 1,834,802 917,401 2,752,204 1,376,102 688,051 2,064,154 1,032,077 3,096,232 1,548,116 774,058 387,029 1,161,088 580,544 290,272 145,136 72,568 36,284 18,142 9,071 27,214 13,607 40,822 20,411 61,234 30,617 91,852 45,926 22,963 68,890 34,445 103,336 51,668 25,834 12,917 38,752 19,376 9,688 4,844 2,422 1,211 3,634 1,817 5,452 2,726 1,363

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