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Atlas › Integer Profiles › Node 48,180,500

48,180,500

22 × 53 × 173 × 557
Abundant Even Composite

48,180,500 factors as 2^2 × 5^3 × 173 × 557. Its 48 positive divisors give a proper-divisor sum of 57,843,964, so this integer is abundant. The Collatz stopping time is 67 steps.

Prime Factor Structure

Factorization String 2^2 × 5^3 × 173 × 557
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 106,024,464
Proper Divisor Sum 57,843,964
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #48180481 ← → #48180527

Radix Representation

Decimal 48180500
Binary 10110111110010110100010100 (26 bits)
Octal 0o267626424
Hexadecimal 0x2DF2D14

Divisor Catalog (48)

1 2 4 5 10 20 25 50 100 125 173 250 346 500 557 692 865 1,114 1,730 2,228 2,785 3,460 4,325 5,570 8,650 11,140 13,925 17,300 21,625 27,850 43,250 55,700 69,625 86,500 96,361 139,250 192,722 278,500 385,444 481,805 963,610 1,927,220 2,409,025 4,818,050 9,636,100 12,045,125 24,090,250 48,180,500

Collatz Trajectory (67 steps to reach 1)

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

48,180,500 24,090,250 12,045,125 36,135,376 18,067,688 9,033,844 4,516,922 2,258,461 6,775,384 3,387,692 1,693,846 846,923 2,540,770 1,270,385 3,811,156 1,905,578 952,789 2,858,368 1,429,184 714,592 357,296 178,648 89,324 44,662 22,331 66,994 33,497 100,492 50,246 25,123 75,370 37,685 113,056 56,528 28,264 14,132 7,066 3,533 10,600 5,300 2,650 1,325 3,976 1,988 994 497 1,492 746 373 1,120 560 280 140 70 35 106 53 160 80 40

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