λ
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Atlas › Integer Profiles › Node 7,200,768

7,200,768

213 × 3 × 293
Abundant Even Composite

7,200,768 factors as 2^13 × 3 × 293. Its 56 positive divisors give a proper-divisor sum of 12,065,640, so this integer is abundant. The Collatz stopping time is 160 steps.

Prime Factor Structure

Factorization String 2^13 × 3 × 293
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 56
Divisor Sum (σ) 19,266,408
Proper Divisor Sum 12,065,640
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #7200763 ← → #7200769

Radix Representation

Decimal 7200768
Binary 11011011110000000000000 (23 bits)
Octal 0o33360000
Hexadecimal 0x6DE000

Divisor Catalog (56)

1 2 3 4 6 8 12 16 24 32 48 64 96 128 192 256 293 384 512 586 768 879 1,024 1,172 1,536 1,758 2,048 2,344 3,072 3,516 4,096 4,688 6,144 7,032 8,192 9,376 12,288 14,064 18,752 24,576 28,128 37,504 56,256 75,008 112,512 150,016 225,024 300,032 450,048 600,064 900,096 1,200,128 1,800,192 2,400,256 3,600,384 7,200,768

Collatz Trajectory (160 steps to reach 1)

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

7,200,768 3,600,384 1,800,192 900,096 450,048 225,024 112,512 56,256 28,128 14,064 7,032 3,516 1,758 879 2,638 1,319 3,958 1,979 5,938 2,969 8,908 4,454 2,227 6,682 3,341 10,024 5,012 2,506 1,253 3,760 1,880 940 470 235 706 353 1,060 530 265 796 398 199 598 299 898 449 1,348 674 337 1,012 506 253 760 380 190 95 286 143 430 215

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