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Atlas › Integer Profiles › Node 3,340,320

3,340,320

25 × 3 × 5 × 6959
Abundant Even Composite

3,340,320 factors as 2^5 × 3 × 5 × 6959. Its 48 positive divisors give a proper-divisor sum of 7,183,200, so this integer is abundant. The Collatz stopping time is 208 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 5 × 6959
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 10,523,520
Proper Divisor Sum 7,183,200
Digit Sum / Digital Root 15 (Root: 6)
Adjacent Primes #3340301 ← → #3340327

Radix Representation

Decimal 3340320
Binary 1100101111100000100000 (22 bits)
Octal 0o14574040
Hexadecimal 0x32F820

Divisor Catalog (48)

1 2 3 4 5 6 8 10 12 15 16 20 24 30 32 40 48 60 80 96 120 160 240 480 6,959 13,918 20,877 27,836 34,795 41,754 55,672 69,590 83,508 104,385 111,344 139,180 167,016 208,770 222,688 278,360 334,032 417,540 556,720 668,064 835,080 1,113,440 1,670,160 3,340,320

Collatz Trajectory (208 steps to reach 1)

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

3,340,320 1,670,160 835,080 417,540 208,770 104,385 313,156 156,578 78,289 234,868 117,434 58,717 176,152 88,076 44,038 22,019 66,058 33,029 99,088 49,544 24,772 12,386 6,193 18,580 9,290 4,645 13,936 6,968 3,484 1,742 871 2,614 1,307 3,922 1,961 5,884 2,942 1,471 4,414 2,207 6,622 3,311 9,934 4,967 14,902 7,451 22,354 11,177 33,532 16,766 8,383 25,150 12,575 37,726 18,863 56,590 28,295 84,886 42,443 127,330

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