768,120

2³ × 3 × 5 × 37 × 173

768,120 factors as 2^3 × 3 × 5 × 37 × 173. Its 64 positive divisors give a proper-divisor sum of 1,612,200, so this integer is abundant. The Collatz stopping time is 149 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 37 × 173

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 2,380,320

Proper Divisor Sum 1,612,200

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #768107 ← → #768127

Radix Representation

Decimal	768120
Binary	10111011100001111000 (20 bits)
Octal	0o2734170
Hexadecimal	0xBB878

Divisor Catalog (60 of 64)

1 2 3 4 5 6 8 10 12 15 20 24 30 37 40 60 74 111 120 148 173 185 222 296 346 370 444 519 555 692 740 865 888 1,038 1,110 1,384 1,480 1,730 2,076 2,220 2,595 3,460 4,152 4,440 5,190 6,401 6,920 10,380 12,802 19,203 20,760 25,604 32,005 38,406 51,208 64,010 76,812 96,015 128,020 153,624

Collatz Trajectory (149 steps to reach 1)

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

768,120 384,060 192,030 96,015 288,046 144,023 432,070 216,035 648,106 324,053 972,160 486,080 243,040 121,520 60,760 30,380 15,190 7,595 22,786 11,393 34,180 17,090 8,545 25,636 12,818 6,409 19,228 9,614 4,807 14,422 7,211 21,634 10,817 32,452 16,226 8,113 24,340 12,170 6,085 18,256 9,128 4,564 2,282 1,141 3,424 1,712 856 428 214 107 322 161 484 242 121 364 182 91 274 137

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