λ
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Atlas › Integer Profiles › Node 37,309,180

37,309,180

22 × 5 × 41 × 173 × 263
Abundant Even Composite

37,309,180 factors as 2^2 × 5 × 41 × 173 × 263. Its 48 positive divisors give a proper-divisor sum of 43,721,924, so this integer is abundant. The Collatz stopping time is 121 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 41 × 173 × 263
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 81,031,104
Proper Divisor Sum 43,721,924
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #37309159 ← → #37309189

Radix Representation

Decimal 37309180
Binary 10001110010100101011111100 (26 bits)
Octal 0o216245374
Hexadecimal 0x2394AFC

Divisor Catalog (48)

1 2 4 5 10 20 41 82 164 173 205 263 346 410 526 692 820 865 1,052 1,315 1,730 2,630 3,460 5,260 7,093 10,783 14,186 21,566 28,372 35,465 43,132 45,499 53,915 70,930 90,998 107,830 141,860 181,996 215,660 227,495 454,990 909,980 1,865,459 3,730,918 7,461,836 9,327,295 18,654,590 37,309,180

Collatz Trajectory (121 steps to reach 1)

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

37,309,180 18,654,590 9,327,295 27,981,886 13,990,943 41,972,830 20,986,415 62,959,246 31,479,623 94,438,870 47,219,435 141,658,306 70,829,153 212,487,460 106,243,730 53,121,865 159,365,596 79,682,798 39,841,399 119,524,198 59,762,099 179,286,298 89,643,149 268,929,448 134,464,724 67,232,362 33,616,181 100,848,544 50,424,272 25,212,136 12,606,068 6,303,034 3,151,517 9,454,552 4,727,276 2,363,638 1,181,819 3,545,458 1,772,729 5,318,188 2,659,094 1,329,547 3,988,642 1,994,321 5,982,964 2,991,482 1,495,741 4,487,224 2,243,612 1,121,806 560,903 1,682,710 841,355 2,524,066 1,262,033 3,786,100 1,893,050 946,525 2,839,576 1,419,788

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