36,967,920

2⁴ × 3 × 5 × 11² × 19 × 67

36,967,920 factors as 2^4 × 3 × 5 × 11^2 × 19 × 67. Its 240 positive divisors give a proper-divisor sum of 97,606,800, so this integer is abundant. The Collatz stopping time is 165 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 5 × 11^2 × 19 × 67

Distinct Prime Factors 6

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 240

Divisor Sum (σ) 134,574,720

Proper Divisor Sum 97,606,800

Digit Sum / Digital Root 42 (Root: 6)

Adjacent Primes #36967913 ← → #36967993

Radix Representation

Decimal	36967920
Binary	10001101000001010111110000 (26 bits)
Octal	0o215012760
Hexadecimal	0x23415F0

Divisor Catalog (60 of 240)

1 2 3 4 5 6 8 10 11 12 15 16 19 20 22 24 30 33 38 40 44 48 55 57 60 66 67 76 80 88 95 110 114 120 121 132 134 152 165 176 190 201 209 220 228 240 242 264 268 285 304 330 335 363 380 402 418 440 456 484

Collatz Trajectory (165 steps to reach 1)

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

36,967,920 18,483,960 9,241,980 4,620,990 2,310,495 6,931,486 3,465,743 10,397,230 5,198,615 15,595,846 7,797,923 23,393,770 11,696,885 35,090,656 17,545,328 8,772,664 4,386,332 2,193,166 1,096,583 3,289,750 1,644,875 4,934,626 2,467,313 7,401,940 3,700,970 1,850,485 5,551,456 2,775,728 1,387,864 693,932 346,966 173,483 520,450 260,225 780,676 390,338 195,169 585,508 292,754 146,377 439,132 219,566 109,783 329,350 164,675 494,026 247,013 741,040 370,520 185,260 92,630 46,315 138,946 69,473 208,420 104,210 52,105 156,316 78,158 39,079

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