48,759,984

2⁴ × 3² × 7 × 13 × 61²

48,759,984 factors as 2^4 × 3^2 × 7 × 13 × 61^2. Its 180 positive divisors give a proper-divisor sum of 121,989,504, so this integer is abundant. The Collatz stopping time is 111 steps.

Prime Factor Structure

Factorization String 2^4 × 3^2 × 7 × 13 × 61^2

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 180

Divisor Sum (σ) 170,749,488

Proper Divisor Sum 121,989,504

Digit Sum / Digital Root 54 (Root: 9)

Adjacent Primes #48759973 ← → #48760001

Radix Representation

Decimal	48759984
Binary	10111010000000010010110000 (26 bits)
Octal	0o272002260
Hexadecimal	0x2E804B0

Divisor Catalog (60 of 180)

1 2 3 4 6 7 8 9 12 13 14 16 18 21 24 26 28 36 39 42 48 52 56 61 63 72 78 84 91 104 112 117 122 126 144 156 168 182 183 208 234 244 252 273 312 336 364 366 427 468 488 504 546 549 624 728 732 793 819 854

Collatz Trajectory (111 steps to reach 1)

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

48,759,984 24,379,992 12,189,996 6,094,998 3,047,499 9,142,498 4,571,249 13,713,748 6,856,874 3,428,437 10,285,312 5,142,656 2,571,328 1,285,664 642,832 321,416 160,708 80,354 40,177 120,532 60,266 30,133 90,400 45,200 22,600 11,300 5,650 2,825 8,476 4,238 2,119 6,358 3,179 9,538 4,769 14,308 7,154 3,577 10,732 5,366 2,683 8,050 4,025 12,076 6,038 3,019 9,058 4,529 13,588 6,794 3,397 10,192 5,096 2,548 1,274 637 1,912 956 478 239

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