4,132,800

2⁶ × 3² × 5² × 7 × 41

4,132,800 factors as 2^6 × 3^2 × 5^2 × 7 × 41. Its 252 positive divisors give a proper-divisor sum of 13,064,016, so this integer is abundant. The Collatz stopping time is 92 steps.

Prime Factor Structure

Factorization String 2^6 × 3^2 × 5^2 × 7 × 41

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 252

Divisor Sum (σ) 17,196,816

Proper Divisor Sum 13,064,016

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #4132783 ← → #4132829

Radix Representation

Decimal	4132800
Binary	1111110000111111000000 (22 bits)
Octal	0o17607700
Hexadecimal	0x3F0FC0

Divisor Catalog (60 of 252)

1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 28 30 32 35 36 40 41 42 45 48 50 56 60 63 64 70 72 75 80 82 84 90 96 100 105 112 120 123 126 140 144 150 160 164 168 175 180 192 200 205 210

Collatz Trajectory (92 steps to reach 1)

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

4,132,800 2,066,400 1,033,200 516,600 258,300 129,150 64,575 193,726 96,863 290,590 145,295 435,886 217,943 653,830 326,915 980,746 490,373 1,471,120 735,560 367,780 183,890 91,945 275,836 137,918 68,959 206,878 103,439 310,318 155,159 465,478 232,739 698,218 349,109 1,047,328 523,664 261,832 130,916 65,458 32,729 98,188 49,094 24,547 73,642 36,821 110,464 55,232 27,616 13,808 6,904 3,452 1,726 863 2,590 1,295 3,886 1,943 5,830 2,915 8,746 4,373

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