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Atlas › Integer Profiles › Node 3,980,100

3,980,100

22 × 3 × 52 × 13267
Abundant Even Composite

3,980,100 factors as 2^2 × 3 × 5^2 × 13267. Its 36 positive divisors give a proper-divisor sum of 7,536,524, so this integer is abundant. The Collatz stopping time is 123 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 5^2 × 13267
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 11,516,624
Proper Divisor Sum 7,536,524
Digit Sum / Digital Root 21 (Root: 3)
Adjacent Primes #3980089 ← → #3980113

Radix Representation

Decimal 3980100
Binary 1111001011101101000100 (22 bits)
Octal 0o17135504
Hexadecimal 0x3CBB44

Divisor Catalog (36)

1 2 3 4 5 6 10 12 15 20 25 30 50 60 75 100 150 300 13,267 26,534 39,801 53,068 66,335 79,602 132,670 159,204 199,005 265,340 331,675 398,010 663,350 796,020 995,025 1,326,700 1,990,050 3,980,100

Collatz Trajectory (123 steps to reach 1)

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

3,980,100 1,990,050 995,025 2,985,076 1,492,538 746,269 2,238,808 1,119,404 559,702 279,851 839,554 419,777 1,259,332 629,666 314,833 944,500 472,250 236,125 708,376 354,188 177,094 88,547 265,642 132,821 398,464 199,232 99,616 49,808 24,904 12,452 6,226 3,113 9,340 4,670 2,335 7,006 3,503 10,510 5,255 15,766 7,883 23,650 11,825 35,476 17,738 8,869 26,608 13,304 6,652 3,326 1,663 4,990 2,495 7,486 3,743 11,230 5,615 16,846 8,423 25,270

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