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Atlas › Integer Profiles › Node 48,867,968

48,867,968

27 × 47 × 8123
Abundant Even Composite

48,867,968 factors as 2^7 × 47 × 8123. Its 32 positive divisors give a proper-divisor sum of 50,569,792, so this integer is abundant. The Collatz stopping time is 106 steps.

Prime Factor Structure

Factorization String 2^7 × 47 × 8123
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 99,437,760
Proper Divisor Sum 50,569,792
Digit Sum / Digital Root 56 (Root: 2)
Adjacent Primes #48867937 ← → #48867971

Radix Representation

Decimal 48867968
Binary 10111010011010101010000000 (26 bits)
Octal 0o272325200
Hexadecimal 0x2E9AA80

Divisor Catalog (32)

1 2 4 8 16 32 47 64 94 128 188 376 752 1,504 3,008 6,016 8,123 16,246 32,492 64,984 129,968 259,936 381,781 519,872 763,562 1,039,744 1,527,124 3,054,248 6,108,496 12,216,992 24,433,984 48,867,968

Collatz Trajectory (106 steps to reach 1)

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

48,867,968 24,433,984 12,216,992 6,108,496 3,054,248 1,527,124 763,562 381,781 1,145,344 572,672 286,336 143,168 71,584 35,792 17,896 8,948 4,474 2,237 6,712 3,356 1,678 839 2,518 1,259 3,778 1,889 5,668 2,834 1,417 4,252 2,126 1,063 3,190 1,595 4,786 2,393 7,180 3,590 1,795 5,386 2,693 8,080 4,040 2,020 1,010 505 1,516 758 379 1,138 569 1,708 854 427 1,282 641 1,924 962 481 1,444

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