λ
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Atlas › Integer Profiles › Node 48,648,220

48,648,220

22 × 5 × 17 × 23 × 6221
Abundant Even Composite

48,648,220 factors as 2^2 × 5 × 17 × 23 × 6221. Its 48 positive divisors give a proper-divisor sum of 64,243,748, so this integer is abundant. The Collatz stopping time is 85 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 17 × 23 × 6221
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 112,891,968
Proper Divisor Sum 64,243,748
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #48648217 ← → #48648233

Radix Representation

Decimal 48648220
Binary 10111001100101000000011100 (26 bits)
Octal 0o271450034
Hexadecimal 0x2E6501C

Divisor Catalog (48)

1 2 4 5 10 17 20 23 34 46 68 85 92 115 170 230 340 391 460 782 1,564 1,955 3,910 6,221 7,820 12,442 24,884 31,105 62,210 105,757 124,420 143,083 211,514 286,166 423,028 528,785 572,332 715,415 1,057,570 1,430,830 2,115,140 2,432,411 2,861,660 4,864,822 9,729,644 12,162,055 24,324,110 48,648,220

Collatz Trajectory (85 steps to reach 1)

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

48,648,220 24,324,110 12,162,055 36,486,166 18,243,083 54,729,250 27,364,625 82,093,876 41,046,938 20,523,469 61,570,408 30,785,204 15,392,602 7,696,301 23,088,904 11,544,452 5,772,226 2,886,113 8,658,340 4,329,170 2,164,585 6,493,756 3,246,878 1,623,439 4,870,318 2,435,159 7,305,478 3,652,739 10,958,218 5,479,109 16,437,328 8,218,664 4,109,332 2,054,666 1,027,333 3,082,000 1,541,000 770,500 385,250 192,625 577,876 288,938 144,469 433,408 216,704 108,352 54,176 27,088 13,544 6,772 3,386 1,693 5,080 2,540 1,270 635 1,906 953 2,860 1,430

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