λ
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Atlas › Integer Profiles › Node 48,801,540

48,801,540

22 × 3 × 5 × 631 × 1289
Abundant Even Composite

48,801,540 factors as 2^2 × 3 × 5 × 631 × 1289. Its 48 positive divisors give a proper-divisor sum of 88,165,500, so this integer is abundant. The Collatz stopping time is 199 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 631 × 1289
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 136,967,040
Proper Divisor Sum 88,165,500
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #48801497 ← → #48801541

Radix Representation

Decimal 48801540
Binary 10111010001010011100000100 (26 bits)
Octal 0o272123404
Hexadecimal 0x2E8A704

Divisor Catalog (48)

1 2 3 4 5 6 10 12 15 20 30 60 631 1,262 1,289 1,893 2,524 2,578 3,155 3,786 3,867 5,156 6,310 6,445 7,572 7,734 9,465 12,620 12,890 15,468 18,930 19,335 25,780 37,860 38,670 77,340 813,359 1,626,718 2,440,077 3,253,436 4,066,795 4,880,154 8,133,590 9,760,308 12,200,385 16,267,180 24,400,770 48,801,540

Collatz Trajectory (199 steps to reach 1)

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

48,801,540 24,400,770 12,200,385 36,601,156 18,300,578 9,150,289 27,450,868 13,725,434 6,862,717 20,588,152 10,294,076 5,147,038 2,573,519 7,720,558 3,860,279 11,580,838 5,790,419 17,371,258 8,685,629 26,056,888 13,028,444 6,514,222 3,257,111 9,771,334 4,885,667 14,657,002 7,328,501 21,985,504 10,992,752 5,496,376 2,748,188 1,374,094 687,047 2,061,142 1,030,571 3,091,714 1,545,857 4,637,572 2,318,786 1,159,393 3,478,180 1,739,090 869,545 2,608,636 1,304,318 652,159 1,956,478 978,239 2,934,718 1,467,359 4,402,078 2,201,039 6,603,118 3,301,559 9,904,678 4,952,339 14,857,018 7,428,509 22,285,528 11,142,764

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