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Atlas › Integer Profiles › Node 36,960,612

36,960,612

22 × 3 × 13 × 47 × 712
Abundant Even Composite

36,960,612 factors as 2^2 × 3 × 13 × 47 × 71^2. Its 72 positive divisors give a proper-divisor sum of 59,245,596, so this integer is abundant. The Collatz stopping time is 103 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 13 × 47 × 71^2
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 96,206,208
Proper Divisor Sum 59,245,596
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #36960611 ← → #36960613

Radix Representation

Decimal 36960612
Binary 10001100111111100101100100 (26 bits)
Octal 0o214774544
Hexadecimal 0x233F964

Divisor Catalog (60 of 72)

1 2 3 4 6 12 13 26 39 47 52 71 78 94 141 142 156 188 213 282 284 426 564 611 852 923 1,222 1,833 1,846 2,444 2,769 3,337 3,666 3,692 5,041 5,538 6,674 7,332 10,011 10,082 11,076 13,348 15,123 20,022 20,164 30,246 40,044 43,381 60,492 65,533 86,762 130,143 131,066 173,524 196,599 236,927 260,286 262,132 393,198 473,854

Collatz Trajectory (103 steps to reach 1)

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

36,960,612 18,480,306 9,240,153 27,720,460 13,860,230 6,930,115 20,790,346 10,395,173 31,185,520 15,592,760 7,796,380 3,898,190 1,949,095 5,847,286 2,923,643 8,770,930 4,385,465 13,156,396 6,578,198 3,289,099 9,867,298 4,933,649 14,800,948 7,400,474 3,700,237 11,100,712 5,550,356 2,775,178 1,387,589 4,162,768 2,081,384 1,040,692 520,346 260,173 780,520 390,260 195,130 97,565 292,696 146,348 73,174 36,587 109,762 54,881 164,644 82,322 41,161 123,484 61,742 30,871 92,614 46,307 138,922 69,461 208,384 104,192 52,096 26,048 13,024 6,512

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