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Atlas › Integer Profiles › Node 6,972,912

6,972,912

24 × 33 × 16141
Abundant Even Composite

6,972,912 factors as 2^4 × 3^3 × 16141. Its 40 positive divisors give a proper-divisor sum of 13,043,168, so this integer is abundant. The Collatz stopping time is 98 steps.

Prime Factor Structure

Factorization String 2^4 × 3^3 × 16141
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 20,016,080
Proper Divisor Sum 13,043,168
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #6972899 ← → #6972961

Radix Representation

Decimal 6972912
Binary 11010100110010111110000 (23 bits)
Octal 0o32462760
Hexadecimal 0x6A65F0

Divisor Catalog (40)

1 2 3 4 6 8 9 12 16 18 24 27 36 48 54 72 108 144 216 432 16,141 32,282 48,423 64,564 96,846 129,128 145,269 193,692 258,256 290,538 387,384 435,807 581,076 774,768 871,614 1,162,152 1,743,228 2,324,304 3,486,456 6,972,912

Collatz Trajectory (98 steps to reach 1)

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

6,972,912 3,486,456 1,743,228 871,614 435,807 1,307,422 653,711 1,961,134 980,567 2,941,702 1,470,851 4,412,554 2,206,277 6,618,832 3,309,416 1,654,708 827,354 413,677 1,241,032 620,516 310,258 155,129 465,388 232,694 116,347 349,042 174,521 523,564 261,782 130,891 392,674 196,337 589,012 294,506 147,253 441,760 220,880 110,440 55,220 27,610 13,805 41,416 20,708 10,354 5,177 15,532 7,766 3,883 11,650 5,825 17,476 8,738 4,369 13,108 6,554 3,277 9,832 4,916 2,458 1,229

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