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Atlas › Integer Profiles › Node 3,322,600

3,322,600

23 × 52 × 37 × 449
Abundant Even Composite

3,322,600 factors as 2^3 × 5^2 × 37 × 449. Its 48 positive divisors give a proper-divisor sum of 4,628,900, so this integer is abundant. The Collatz stopping time is 177 steps.

Prime Factor Structure

Factorization String 2^3 × 5^2 × 37 × 449
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 7,951,500
Proper Divisor Sum 4,628,900
Digit Sum / Digital Root 16 (Root: 7)
Adjacent Primes #3322577 ← → #3322607

Radix Representation

Decimal 3322600
Binary 1100101011001011101000 (22 bits)
Octal 0o14531350
Hexadecimal 0x32B2E8

Divisor Catalog (48)

1 2 4 5 8 10 20 25 37 40 50 74 100 148 185 200 296 370 449 740 898 925 1,480 1,796 1,850 2,245 3,592 3,700 4,490 7,400 8,980 11,225 16,613 17,960 22,450 33,226 44,900 66,452 83,065 89,800 132,904 166,130 332,260 415,325 664,520 830,650 1,661,300 3,322,600

Collatz Trajectory (177 steps to reach 1)

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

3,322,600 1,661,300 830,650 415,325 1,245,976 622,988 311,494 155,747 467,242 233,621 700,864 350,432 175,216 87,608 43,804 21,902 10,951 32,854 16,427 49,282 24,641 73,924 36,962 18,481 55,444 27,722 13,861 41,584 20,792 10,396 5,198 2,599 7,798 3,899 11,698 5,849 17,548 8,774 4,387 13,162 6,581 19,744 9,872 4,936 2,468 1,234 617 1,852 926 463 1,390 695 2,086 1,043 3,130 1,565 4,696 2,348 1,174 587

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