λ
Ratio Atlas
Atlas › Integer Profiles › Node 76,012,008

76,012,008

23 × 3 × 19 × 166693
Abundant Even Composite

76,012,008 factors as 2^3 × 3 × 19 × 166693. Its 32 positive divisors give a proper-divisor sum of 124,020,792, so this integer is abundant. The Collatz stopping time is 272 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 19 × 166693
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 200,032,800
Proper Divisor Sum 124,020,792
Digit Sum / Digital Root 24 (Root: 6)
Adjacent Primes #76012007 ← → #76012037

Radix Representation

Decimal 76012008
Binary 100100001111101100111101000 (27 bits)
Octal 0o441754750
Hexadecimal 0x487D9E8

Divisor Catalog (32)

1 2 3 4 6 8 12 19 24 38 57 76 114 152 228 456 166,693 333,386 500,079 666,772 1,000,158 1,333,544 2,000,316 3,167,167 4,000,632 6,334,334 9,501,501 12,668,668 19,003,002 25,337,336 38,006,004 76,012,008

Collatz Trajectory (272 steps to reach 1)

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

76,012,008 38,006,004 19,003,002 9,501,501 28,504,504 14,252,252 7,126,126 3,563,063 10,689,190 5,344,595 16,033,786 8,016,893 24,050,680 12,025,340 6,012,670 3,006,335 9,019,006 4,509,503 13,528,510 6,764,255 20,292,766 10,146,383 30,439,150 15,219,575 45,658,726 22,829,363 68,488,090 34,244,045 102,732,136 51,366,068 25,683,034 12,841,517 38,524,552 19,262,276 9,631,138 4,815,569 14,446,708 7,223,354 3,611,677 10,835,032 5,417,516 2,708,758 1,354,379 4,063,138 2,031,569 6,094,708 3,047,354 1,523,677 4,571,032 2,285,516 1,142,758 571,379 1,714,138 857,069 2,571,208 1,285,604 642,802 321,401 964,204 482,102

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