48,759,900

2² × 3 × 5² × 7² × 31 × 107

48,759,900 factors as 2^2 × 3 × 5^2 × 7^2 × 31 × 107. Its 216 positive divisors give a proper-divisor sum of 122,229,156, so this integer is abundant. The Collatz stopping time is 93 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 5^2 × 7^2 × 31 × 107

Distinct Prime Factors 6

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 216

Divisor Sum (σ) 170,989,056

Proper Divisor Sum 122,229,156

Digit Sum / Digital Root 42 (Root: 6)

Adjacent Primes #48759899 ← → #48759913

Radix Representation

Decimal	48759900
Binary	10111010000000010001011100 (26 bits)
Octal	0o272002134
Hexadecimal	0x2E8045C

Divisor Catalog (60 of 216)

1 2 3 4 5 6 7 10 12 14 15 20 21 25 28 30 31 35 42 49 50 60 62 70 75 84 93 98 100 105 107 124 140 147 150 155 175 186 196 210 214 217 245 294 300 310 321 350 372 420 428 434 465 490 525 535 588 620 642 651

Collatz Trajectory (93 steps to reach 1)

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

48,759,900 24,379,950 12,189,975 36,569,926 18,284,963 54,854,890 27,427,445 82,282,336 41,141,168 20,570,584 10,285,292 5,142,646 2,571,323 7,713,970 3,856,985 11,570,956 5,785,478 2,892,739 8,678,218 4,339,109 13,017,328 6,508,664 3,254,332 1,627,166 813,583 2,440,750 1,220,375 3,661,126 1,830,563 5,491,690 2,745,845 8,237,536 4,118,768 2,059,384 1,029,692 514,846 257,423 772,270 386,135 1,158,406 579,203 1,737,610 868,805 2,606,416 1,303,208 651,604 325,802 162,901 488,704 244,352 122,176 61,088 30,544 15,272 7,636 3,818 1,909 5,728 2,864 1,432

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