177,975

3² × 5² × 7 × 113

177,975 factors as 3^2 × 5^2 × 7 × 113. Its 36 positive divisors give a proper-divisor sum of 189,561, so this integer is abundant. The Collatz stopping time is 95 steps.

Prime Factor Structure

Factorization String 3^2 × 5^2 × 7 × 113

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 367,536

Proper Divisor Sum 189,561

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #177967 ← → #177979

Radix Representation

Decimal	177975
Binary	101011011100110111 (18 bits)
Octal	0o533467
Hexadecimal	0x2B737

Divisor Catalog (36)

1 3 5 7 9 15 21 25 35 45 63 75 105 113 175 225 315 339 525 565 791 1,017 1,575 1,695 2,373 2,825 3,955 5,085 7,119 8,475 11,865 19,775 25,425 35,595 59,325 177,975

Collatz Trajectory (95 steps to reach 1)

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

177,975 533,926 266,963 800,890 400,445 1,201,336 600,668 300,334 150,167 450,502 225,251 675,754 337,877 1,013,632 506,816 253,408 126,704 63,352 31,676 15,838 7,919 23,758 11,879 35,638 17,819 53,458 26,729 80,188 40,094 20,047 60,142 30,071 90,214 45,107 135,322 67,661 202,984 101,492 50,746 25,373 76,120 38,060 19,030 9,515 28,546 14,273 42,820 21,410 10,705 32,116 16,058 8,029 24,088 12,044 6,022 3,011 9,034 4,517 13,552 6,776

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