λ
Zalai Atlas

7,780,050

2 × 34 × 52 × 17 × 113
Abundant Even Composite

7,780,050 has the prime decomposition 2 × 3^4 × 5^2 × 17 × 113. Its 5 distinct prime factors produce 120 positive divisors.

Prime Factor Structure

Factorization String 2 × 3^4 × 5^2 × 17 × 113
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 120
Divisor Sum (σ) 23,091,156
Proper Divisor Sum 15,311,106
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #7780043 ← → #7780061

Radix Representation

Decimal 7780050
Binary 11101101011011011010010 (23 bits)
Octal 0o35533322
Hexadecimal 0x76B6D2

Divisor Catalog (60 of 120)

1 2 3 5 6 9 10 15 17 18 25 27 30 34 45 50 51 54 75 81 85 90 102 113 135 150 153 162 170 225 226 255 270 306 339 405 425 450 459 510 565 675 678 765 810 850 918 1,017 1,130 1,275 1,350 1,377 1,530 1,695 1,921 2,025 2,034 2,295 2,550 2,754

Collatz Trajectory (186 steps to reach 1)

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

7,780,050 3,890,025 11,670,076 5,835,038 2,917,519 8,752,558 4,376,279 13,128,838 6,564,419 19,693,258 9,846,629 29,539,888 14,769,944 7,384,972 3,692,486 1,846,243 5,538,730 2,769,365 8,308,096 4,154,048 2,077,024 1,038,512 519,256 259,628 129,814 64,907 194,722 97,361 292,084 146,042 73,021 219,064 109,532 54,766 27,383 82,150 41,075 123,226 61,613 184,840 92,420 46,210 23,105 69,316 34,658 17,329 51,988 25,994 12,997 38,992 19,496 9,748 4,874 2,437 7,312 3,656 1,828 914 457 1,372

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