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Atlas › Integer Profiles › Node 48,769,840

48,769,840

24 × 5 × 7 × 73 × 1193
Abundant Even Composite

48,769,840 factors as 2^4 × 5 × 7 × 73 × 1193. Its 80 positive divisors give a proper-divisor sum of 82,703,888, so this integer is abundant. The Collatz stopping time is 85 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 7 × 73 × 1193
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 131,473,728
Proper Divisor Sum 82,703,888
Digit Sum / Digital Root 46 (Root: 1)
Adjacent Primes #48769823 ← → #48769841

Radix Representation

Decimal 48769840
Binary 10111010000010101100110000 (26 bits)
Octal 0o272025460
Hexadecimal 0x2E82B30

Divisor Catalog (60 of 80)

1 2 4 5 7 8 10 14 16 20 28 35 40 56 70 73 80 112 140 146 280 292 365 511 560 584 730 1,022 1,168 1,193 1,460 2,044 2,386 2,555 2,920 4,088 4,772 5,110 5,840 5,965 8,176 8,351 9,544 10,220 11,930 16,702 19,088 20,440 23,860 33,404 40,880 41,755 47,720 66,808 83,510 87,089 95,440 133,616 167,020 174,178

Collatz Trajectory (85 steps to reach 1)

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

48,769,840 24,384,920 12,192,460 6,096,230 3,048,115 9,144,346 4,572,173 13,716,520 6,858,260 3,429,130 1,714,565 5,143,696 2,571,848 1,285,924 642,962 321,481 964,444 482,222 241,111 723,334 361,667 1,085,002 542,501 1,627,504 813,752 406,876 203,438 101,719 305,158 152,579 457,738 228,869 686,608 343,304 171,652 85,826 42,913 128,740 64,370 32,185 96,556 48,278 24,139 72,418 36,209 108,628 54,314 27,157 81,472 40,736 20,368 10,184 5,092 2,546 1,273 3,820 1,910 955 2,866 1,433

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