98,175

3 × 5² × 7 × 11 × 17

98,175 factors as 3 × 5^2 × 7 × 11 × 17. Its 48 positive divisors give a proper-divisor sum of 116,097, so this integer is abundant. The Collatz stopping time is 71 steps.

Prime Factor Structure

Factorization String 3 × 5^2 × 7 × 11 × 17

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 214,272

Proper Divisor Sum 116,097

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #98143 ← → #98179

Radix Representation

Decimal	98175
Binary	10111111101111111 (17 bits)
Octal	0o277577
Hexadecimal	0x17F7F

Divisor Catalog (48)

1 3 5 7 11 15 17 21 25 33 35 51 55 75 77 85 105 119 165 175 187 231 255 275 357 385 425 525 561 595 825 935 1,155 1,275 1,309 1,785 1,925 2,805 2,975 3,927 4,675 5,775 6,545 8,925 14,025 19,635 32,725 98,175

Collatz Trajectory (71 steps to reach 1)

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

98,175 294,526 147,263 441,790 220,895 662,686 331,343 994,030 497,015 1,491,046 745,523 2,236,570 1,118,285 3,354,856 1,677,428 838,714 419,357 1,258,072 629,036 314,518 157,259 471,778 235,889 707,668 353,834 176,917 530,752 265,376 132,688 66,344 33,172 16,586 8,293 24,880 12,440 6,220 3,110 1,555 4,666 2,333 7,000 3,500 1,750 875 2,626 1,313 3,940 1,970 985 2,956 1,478 739 2,218 1,109 3,328 1,664 832 416 208 104

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