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Atlas › Integer Profiles › Node 72,077,120

72,077,120

26 × 5 × 225241
Abundant Even Composite

72,077,120 factors as 2^6 × 5 × 225241. Its 28 positive divisors give a proper-divisor sum of 99,557,284, so this integer is abundant. The Collatz stopping time is 259 steps.

Prime Factor Structure

Factorization String 2^6 × 5 × 225241
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 28
Divisor Sum (σ) 171,634,404
Proper Divisor Sum 99,557,284
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #72077119 ← → #72077149

Radix Representation

Decimal 72077120
Binary 100010010111100111101000000 (27 bits)
Octal 0o422747500
Hexadecimal 0x44BCF40

Divisor Catalog (28)

1 2 4 5 8 10 16 20 32 40 64 80 160 320 225,241 450,482 900,964 1,126,205 1,801,928 2,252,410 3,603,856 4,504,820 7,207,712 9,009,640 14,415,424 18,019,280 36,038,560 72,077,120

Collatz Trajectory (259 steps to reach 1)

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

72,077,120 36,038,560 18,019,280 9,009,640 4,504,820 2,252,410 1,126,205 3,378,616 1,689,308 844,654 422,327 1,266,982 633,491 1,900,474 950,237 2,850,712 1,425,356 712,678 356,339 1,069,018 534,509 1,603,528 801,764 400,882 200,441 601,324 300,662 150,331 450,994 225,497 676,492 338,246 169,123 507,370 253,685 761,056 380,528 190,264 95,132 47,566 23,783 71,350 35,675 107,026 53,513 160,540 80,270 40,135 120,406 60,203 180,610 90,305 270,916 135,458 67,729 203,188 101,594 50,797 152,392 76,196

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