λ
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Atlas › Integer Profiles › Node 72,088,968

72,088,968

23 × 3 × 7 × 429101
Abundant Even Composite

72,088,968 factors as 2^3 × 3 × 7 × 429101. Its 32 positive divisors give a proper-divisor sum of 133,879,992, so this integer is abundant. The Collatz stopping time is 153 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 7 × 429101
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 205,968,960
Proper Divisor Sum 133,879,992
Digit Sum / Digital Root 48 (Root: 3)
Adjacent Primes #72088967 ← → #72088997

Radix Representation

Decimal 72088968
Binary 100010010111111110110001000 (27 bits)
Octal 0o422776610
Hexadecimal 0x44BFD88

Divisor Catalog (32)

1 2 3 4 6 7 8 12 14 21 24 28 42 56 84 168 429,101 858,202 1,287,303 1,716,404 2,574,606 3,003,707 3,432,808 5,149,212 6,007,414 9,011,121 10,298,424 12,014,828 18,022,242 24,029,656 36,044,484 72,088,968

Collatz Trajectory (153 steps to reach 1)

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

72,088,968 36,044,484 18,022,242 9,011,121 27,033,364 13,516,682 6,758,341 20,275,024 10,137,512 5,068,756 2,534,378 1,267,189 3,801,568 1,900,784 950,392 475,196 237,598 118,799 356,398 178,199 534,598 267,299 801,898 400,949 1,202,848 601,424 300,712 150,356 75,178 37,589 112,768 56,384 28,192 14,096 7,048 3,524 1,762 881 2,644 1,322 661 1,984 992 496 248 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364

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