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Atlas › Integer Profiles › Node 31,377,940

31,377,940

22 × 5 × 11 × 193 × 739
Abundant Even Composite

31,377,940 factors as 2^2 × 5 × 11 × 193 × 739. Its 48 positive divisors give a proper-divisor sum of 40,976,300, so this integer is abundant. The Collatz stopping time is 157 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 11 × 193 × 739
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 72,354,240
Proper Divisor Sum 40,976,300
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #31377923 ← → #31377943

Radix Representation

Decimal 31377940
Binary 1110111101100101000010100 (25 bits)
Octal 0o167545024
Hexadecimal 0x1DECA14

Divisor Catalog (48)

1 2 4 5 10 11 20 22 44 55 110 193 220 386 739 772 965 1,478 1,930 2,123 2,956 3,695 3,860 4,246 7,390 8,129 8,492 10,615 14,780 16,258 21,230 32,516 40,645 42,460 81,290 142,627 162,580 285,254 570,508 713,135 1,426,270 1,568,897 2,852,540 3,137,794 6,275,588 7,844,485 15,688,970 31,377,940

Collatz Trajectory (157 steps to reach 1)

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

31,377,940 15,688,970 7,844,485 23,533,456 11,766,728 5,883,364 2,941,682 1,470,841 4,412,524 2,206,262 1,103,131 3,309,394 1,654,697 4,964,092 2,482,046 1,241,023 3,723,070 1,861,535 5,584,606 2,792,303 8,376,910 4,188,455 12,565,366 6,282,683 18,848,050 9,424,025 28,272,076 14,136,038 7,068,019 21,204,058 10,602,029 31,806,088 15,903,044 7,951,522 3,975,761 11,927,284 5,963,642 2,981,821 8,945,464 4,472,732 2,236,366 1,118,183 3,354,550 1,677,275 5,031,826 2,515,913 7,547,740 3,773,870 1,886,935 5,660,806 2,830,403 8,491,210 4,245,605 12,736,816 6,368,408 3,184,204 1,592,102 796,051 2,388,154 1,194,077

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