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Atlas › Integer Profiles › Node 6,748,872

6,748,872

23 × 3 × 13 × 97 × 223
Abundant Even Composite

6,748,872 factors as 2^3 × 3 × 13 × 97 × 223. Its 64 positive divisors give a proper-divisor sum of 11,690,808, so this integer is abundant. The Collatz stopping time is 178 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 13 × 97 × 223
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 18,439,680
Proper Divisor Sum 11,690,808
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #6748849 ← → #6748883

Radix Representation

Decimal 6748872
Binary 11001101111101011001000 (23 bits)
Octal 0o31575310
Hexadecimal 0x66FAC8

Divisor Catalog (60 of 64)

1 2 3 4 6 8 12 13 24 26 39 52 78 97 104 156 194 223 291 312 388 446 582 669 776 892 1,164 1,261 1,338 1,784 2,328 2,522 2,676 2,899 3,783 5,044 5,352 5,798 7,566 8,697 10,088 11,596 15,132 17,394 21,631 23,192 30,264 34,788 43,262 64,893 69,576 86,524 129,786 173,048 259,572 281,203 519,144 562,406 843,609 1,124,812

Collatz Trajectory (178 steps to reach 1)

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

6,748,872 3,374,436 1,687,218 843,609 2,530,828 1,265,414 632,707 1,898,122 949,061 2,847,184 1,423,592 711,796 355,898 177,949 533,848 266,924 133,462 66,731 200,194 100,097 300,292 150,146 75,073 225,220 112,610 56,305 168,916 84,458 42,229 126,688 63,344 31,672 15,836 7,918 3,959 11,878 5,939 17,818 8,909 26,728 13,364 6,682 3,341 10,024 5,012 2,506 1,253 3,760 1,880 940 470 235 706 353 1,060 530 265 796 398 199

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