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Atlas › Integer Profiles › Node 48,936,768

48,936,768

26 × 3 × 254879
Abundant Even Composite

48,936,768 factors as 2^6 × 3 × 254879. Its 28 positive divisors give a proper-divisor sum of 80,542,272, so this integer is abundant. The Collatz stopping time is 111 steps.

Prime Factor Structure

Factorization String 2^6 × 3 × 254879
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 28
Divisor Sum (σ) 129,479,040
Proper Divisor Sum 80,542,272
Digit Sum / Digital Root 51 (Root: 6)
Adjacent Primes #48936763 ← → #48936773

Radix Representation

Decimal 48936768
Binary 10111010101011011101000000 (26 bits)
Octal 0o272533500
Hexadecimal 0x2EAB740

Divisor Catalog (28)

1 2 3 4 6 8 12 16 24 32 48 64 96 192 254,879 509,758 764,637 1,019,516 1,529,274 2,039,032 3,058,548 4,078,064 6,117,096 8,156,128 12,234,192 16,312,256 24,468,384 48,936,768

Collatz Trajectory (111 steps to reach 1)

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

48,936,768 24,468,384 12,234,192 6,117,096 3,058,548 1,529,274 764,637 2,293,912 1,146,956 573,478 286,739 860,218 430,109 1,290,328 645,164 322,582 161,291 483,874 241,937 725,812 362,906 181,453 544,360 272,180 136,090 68,045 204,136 102,068 51,034 25,517 76,552 38,276 19,138 9,569 28,708 14,354 7,177 21,532 10,766 5,383 16,150 8,075 24,226 12,113 36,340 18,170 9,085 27,256 13,628 6,814 3,407 10,222 5,111 15,334 7,667 23,002 11,501 34,504 17,252 8,626

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