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Atlas › Integer Profiles › Node 37,779,196

37,779,196

22 × 72 × 13 × 14827
Abundant Even Composite

37,779,196 factors as 2^2 × 7^2 × 13 × 14827. Its 36 positive divisors give a proper-divisor sum of 45,050,012, so this integer is abundant. The Collatz stopping time is 364 steps.

Prime Factor Structure

Factorization String 2^2 × 7^2 × 13 × 14827
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 82,829,208
Proper Divisor Sum 45,050,012
Digit Sum / Digital Root 49 (Root: 4)
Adjacent Primes #37779169 ← → #37779197

Radix Representation

Decimal 37779196
Binary 10010000000111011011111100 (26 bits)
Octal 0o220073374
Hexadecimal 0x24076FC

Divisor Catalog (36)

1 2 4 7 13 14 26 28 49 52 91 98 182 196 364 637 1,274 2,548 14,827 29,654 59,308 103,789 192,751 207,578 385,502 415,156 726,523 771,004 1,349,257 1,453,046 2,698,514 2,906,092 5,397,028 9,444,799 18,889,598 37,779,196

Collatz Trajectory (364 steps to reach 1)

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

37,779,196 18,889,598 9,444,799 28,334,398 14,167,199 42,501,598 21,250,799 63,752,398 31,876,199 95,628,598 47,814,299 143,442,898 71,721,449 215,164,348 107,582,174 53,791,087 161,373,262 80,686,631 242,059,894 121,029,947 363,089,842 181,544,921 544,634,764 272,317,382 136,158,691 408,476,074 204,238,037 612,714,112 306,357,056 153,178,528 76,589,264 38,294,632 19,147,316 9,573,658 4,786,829 14,360,488 7,180,244 3,590,122 1,795,061 5,385,184 2,692,592 1,346,296 673,148 336,574 168,287 504,862 252,431 757,294 378,647 1,135,942 567,971 1,703,914 851,957 2,555,872 1,277,936 638,968 319,484 159,742 79,871 239,614

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