47,748,680

2³ × 5 × 7 × 31 × 5501

47,748,680 factors as 2^3 × 5 × 7 × 31 × 5501. Its 64 positive divisors give a proper-divisor sum of 79,017,400, so this integer is abundant. The Collatz stopping time is 124 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 7 × 31 × 5501

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 126,766,080

Proper Divisor Sum 79,017,400

Digit Sum / Digital Root 44 (Root: 8)

Adjacent Primes #47748661 ← → #47748683

Radix Representation

Decimal	47748680
Binary	10110110001001011001001000 (26 bits)
Octal	0o266113110
Hexadecimal	0x2D89648

Divisor Catalog (60 of 64)

1 2 4 5 7 8 10 14 20 28 31 35 40 56 62 70 124 140 155 217 248 280 310 434 620 868 1,085 1,240 1,736 2,170 4,340 5,501 8,680 11,002 22,004 27,505 38,507 44,008 55,010 77,014 110,020 154,028 170,531 192,535 220,040 308,056 341,062 385,070 682,124 770,140 852,655 1,193,717 1,364,248 1,540,280 1,705,310 2,387,434 3,410,620 4,774,868 5,968,585 6,821,240

Collatz Trajectory (124 steps to reach 1)

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

47,748,680 23,874,340 11,937,170 5,968,585 17,905,756 8,952,878 4,476,439 13,429,318 6,714,659 20,143,978 10,071,989 30,215,968 15,107,984 7,553,992 3,776,996 1,888,498 944,249 2,832,748 1,416,374 708,187 2,124,562 1,062,281 3,186,844 1,593,422 796,711 2,390,134 1,195,067 3,585,202 1,792,601 5,377,804 2,688,902 1,344,451 4,033,354 2,016,677 6,050,032 3,025,016 1,512,508 756,254 378,127 1,134,382 567,191 1,701,574 850,787 2,552,362 1,276,181 3,828,544 1,914,272 957,136 478,568 239,284 119,642 59,821 179,464 89,732 44,866 22,433 67,300 33,650 16,825 50,476

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