177,940

2² × 5 × 7 × 31 × 41

177,940 factors as 2^2 × 5 × 7 × 31 × 41. Its 48 positive divisors give a proper-divisor sum of 273,644, so this integer is abundant. The Collatz stopping time is 134 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 7 × 31 × 41

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 451,584

Proper Divisor Sum 273,644

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #177929 ← → #177943

Radix Representation

Decimal	177940
Binary	101011011100010100 (18 bits)
Octal	0o533424
Hexadecimal	0x2B714

Divisor Catalog (48)

1 2 4 5 7 10 14 20 28 31 35 41 62 70 82 124 140 155 164 205 217 287 310 410 434 574 620 820 868 1,085 1,148 1,271 1,435 2,170 2,542 2,870 4,340 5,084 5,740 6,355 8,897 12,710 17,794 25,420 35,588 44,485 88,970 177,940

Collatz Trajectory (134 steps to reach 1)

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

177,940 88,970 44,485 133,456 66,728 33,364 16,682 8,341 25,024 12,512 6,256 3,128 1,564 782 391 1,174 587 1,762 881 2,644 1,322 661 1,984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1,186

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