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Atlas › Integer Profiles › Node 77,854,304

77,854,304

25 × 112 × 20107
Abundant Even Composite

77,854,304 factors as 2^5 × 11^2 × 20107. Its 36 positive divisors give a proper-divisor sum of 90,630,628, so this integer is abundant. The Collatz stopping time is 166 steps.

Prime Factor Structure

Factorization String 2^5 × 11^2 × 20107
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 168,484,932
Proper Divisor Sum 90,630,628
Digit Sum / Digital Root 38 (Root: 2)
Adjacent Primes #77854291 ← → #77854307

Radix Representation

Decimal 77854304
Binary 100101000111111011001100000 (27 bits)
Octal 0o450773140
Hexadecimal 0x4A3F660

Divisor Catalog (36)

1 2 4 8 11 16 22 32 44 88 121 176 242 352 484 968 1,936 3,872 20,107 40,214 80,428 160,856 221,177 321,712 442,354 643,424 884,708 1,769,416 2,432,947 3,538,832 4,865,894 7,077,664 9,731,788 19,463,576 38,927,152 77,854,304

Collatz Trajectory (166 steps to reach 1)

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

77,854,304 38,927,152 19,463,576 9,731,788 4,865,894 2,432,947 7,298,842 3,649,421 10,948,264 5,474,132 2,737,066 1,368,533 4,105,600 2,052,800 1,026,400 513,200 256,600 128,300 64,150 32,075 96,226 48,113 144,340 72,170 36,085 108,256 54,128 27,064 13,532 6,766 3,383 10,150 5,075 15,226 7,613 22,840 11,420 5,710 2,855 8,566 4,283 12,850 6,425 19,276 9,638 4,819 14,458 7,229 21,688 10,844 5,422 2,711 8,134 4,067 12,202 6,101 18,304 9,152 4,576 2,288

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