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Atlas › Integer Profiles › Node 37,293,132

37,293,132

22 × 3 × 53 × 191 × 307
Abundant Even Composite

37,293,132 factors as 2^2 × 3 × 53 × 191 × 307. Its 48 positive divisors give a proper-divisor sum of 52,120,500, so this integer is abundant. The Collatz stopping time is 196 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 53 × 191 × 307
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 89,413,632
Proper Divisor Sum 52,120,500
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #37293103 ← → #37293167

Radix Representation

Decimal 37293132
Binary 10001110010000110001001100 (26 bits)
Octal 0o216206114
Hexadecimal 0x2390C4C

Divisor Catalog (48)

1 2 3 4 6 12 53 106 159 191 212 307 318 382 573 614 636 764 921 1,146 1,228 1,842 2,292 3,684 10,123 16,271 20,246 30,369 32,542 40,492 48,813 58,637 60,738 65,084 97,626 117,274 121,476 175,911 195,252 234,548 351,822 703,644 3,107,761 6,215,522 9,323,283 12,431,044 18,646,566 37,293,132

Collatz Trajectory (196 steps to reach 1)

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

37,293,132 18,646,566 9,323,283 27,969,850 13,984,925 41,954,776 20,977,388 10,488,694 5,244,347 15,733,042 7,866,521 23,599,564 11,799,782 5,899,891 17,699,674 8,849,837 26,549,512 13,274,756 6,637,378 3,318,689 9,956,068 4,978,034 2,489,017 7,467,052 3,733,526 1,866,763 5,600,290 2,800,145 8,400,436 4,200,218 2,100,109 6,300,328 3,150,164 1,575,082 787,541 2,362,624 1,181,312 590,656 295,328 147,664 73,832 36,916 18,458 9,229 27,688 13,844 6,922 3,461 10,384 5,192 2,596 1,298 649 1,948 974 487 1,462 731 2,194 1,097

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