3,772,800

2⁷ × 3² × 5² × 131

3,772,800 has the prime decomposition 2^7 × 3^2 × 5^2 × 131. Its 4 distinct prime factors produce 144 positive divisors.

Prime Factor Structure

Factorization String 2^7 × 3^2 × 5^2 × 131

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 144

Divisor Sum (σ) 13,564,980

Proper Divisor Sum 9,792,180

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #3772771 ← → #3772801

Radix Representation

Decimal	3772800
Binary	1110011001000110000000 (22 bits)
Octal	0o16310600
Hexadecimal	0x399180

Divisor Catalog (60 of 144)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 32 36 40 45 48 50 60 64 72 75 80 90 96 100 120 128 131 144 150 160 180 192 200 225 240 262 288 300 320 360 384 393 400 450 480 524 576 600 640 655 720 786 800

Collatz Trajectory (53 steps to reach 1)

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

3,772,800 1,886,400 943,200 471,600 235,800 117,900 58,950 29,475 88,426 44,213 132,640 66,320 33,160 16,580 8,290 4,145 12,436 6,218 3,109 9,328 4,664 2,332 1,166 583 1,750 875 2,626 1,313 3,940 1,970 985 2,956 1,478 739 2,218 1,109 3,328 1,664 832 416 208 104 52 26 13 40 20 10 5 16 8 4 2 1

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