76,140

2² × 3⁴ × 5 × 47

For 76,140, the 60 positive divisors have a total of 243,936. Removing 76,140 leaves 167,796, which gives the abundant classification.

Prime Factor Structure

Factorization String 2^2 × 3^4 × 5 × 47

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 60

Divisor Sum (σ) 243,936

Proper Divisor Sum 167,796

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #76129 ← → #76147

Radix Representation

Decimal	76140
Binary	10010100101101100 (17 bits)
Octal	0o224554
Hexadecimal	0x1296C

Divisor Catalog (60)

1 2 3 4 5 6 9 10 12 15 18 20 27 30 36 45 47 54 60 81 90 94 108 135 141 162 180 188 235 270 282 324 405 423 470 540 564 705 810 846 940 1,269 1,410 1,620 1,692 2,115 2,538 2,820 3,807 4,230 5,076 6,345 7,614 8,460 12,690 15,228 19,035 25,380 38,070 76,140

Collatz Trajectory (94 steps to reach 1)

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

76,140 38,070 19,035 57,106 28,553 85,660 42,830 21,415 64,246 32,123 96,370 48,185 144,556 72,278 36,139 108,418 54,209 162,628 81,314 40,657 121,972 60,986 30,493 91,480 45,740 22,870 11,435 34,306 17,153 51,460 25,730 12,865 38,596 19,298 9,649 28,948 14,474 7,237 21,712 10,856 5,428 2,714 1,357 4,072 2,036 1,018 509 1,528 764 382 191 574 287 862 431 1,294 647 1,942 971 2,914

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