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Ratio Atlas
Atlas › Integer Profiles › Node 78,055,152

78,055,152

24 × 3 × 7 × 232307
Abundant Even Composite

78,055,152 factors as 2^4 × 3 × 7 × 232307. Its 40 positive divisors give a proper-divisor sum of 152,394,384, so this integer is abundant. The Collatz stopping time is 272 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 7 × 232307
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 230,449,536
Proper Divisor Sum 152,394,384
Digit Sum / Digital Root 33 (Root: 6)
Adjacent Primes #78055147 ← → #78055189

Radix Representation

Decimal 78055152
Binary 100101001110000011011110000 (27 bits)
Octal 0o451603360
Hexadecimal 0x4A706F0

Divisor Catalog (40)

1 2 3 4 6 7 8 12 14 16 21 24 28 42 48 56 84 112 168 336 232,307 464,614 696,921 929,228 1,393,842 1,626,149 1,858,456 2,787,684 3,252,298 3,716,912 4,878,447 5,575,368 6,504,596 9,756,894 11,150,736 13,009,192 19,513,788 26,018,384 39,027,576 78,055,152

Collatz Trajectory (272 steps to reach 1)

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

78,055,152 39,027,576 19,513,788 9,756,894 4,878,447 14,635,342 7,317,671 21,953,014 10,976,507 32,929,522 16,464,761 49,394,284 24,697,142 12,348,571 37,045,714 18,522,857 55,568,572 27,784,286 13,892,143 41,676,430 20,838,215 62,514,646 31,257,323 93,771,970 46,885,985 140,657,956 70,328,978 35,164,489 105,493,468 52,746,734 26,373,367 79,120,102 39,560,051 118,680,154 59,340,077 178,020,232 89,010,116 44,505,058 22,252,529 66,757,588 33,378,794 16,689,397 50,068,192 25,034,096 12,517,048 6,258,524 3,129,262 1,564,631 4,693,894 2,346,947 7,040,842 3,520,421 10,561,264 5,280,632 2,640,316 1,320,158 660,079 1,980,238 990,119 2,970,358

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