7,672,800

2⁵ × 3 × 5² × 23 × 139

7,672,800 factors as 2^5 × 3 × 5^2 × 23 × 139. Its 144 positive divisors give a proper-divisor sum of 18,575,520, so this integer is abundant. The Collatz stopping time is 124 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 5^2 × 23 × 139

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 144

Divisor Sum (σ) 26,248,320

Proper Divisor Sum 18,575,520

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #7672799 ← → #7672853

Radix Representation

Decimal	7672800
Binary	11101010001001111100000 (23 bits)
Octal	0o35211740
Hexadecimal	0x7513E0

Divisor Catalog (60 of 144)

1 2 3 4 5 6 8 10 12 15 16 20 23 24 25 30 32 40 46 48 50 60 69 75 80 92 96 100 115 120 138 139 150 160 184 200 230 240 276 278 300 345 368 400 417 460 480 552 556 575 600 690 695 736 800 834 920 1,104 1,112 1,150

Collatz Trajectory (124 steps to reach 1)

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

7,672,800 3,836,400 1,918,200 959,100 479,550 239,775 719,326 359,663 1,078,990 539,495 1,618,486 809,243 2,427,730 1,213,865 3,641,596 1,820,798 910,399 2,731,198 1,365,599 4,096,798 2,048,399 6,145,198 3,072,599 9,217,798 4,608,899 13,826,698 6,913,349 20,740,048 10,370,024 5,185,012 2,592,506 1,296,253 3,888,760 1,944,380 972,190 486,095 1,458,286 729,143 2,187,430 1,093,715 3,281,146 1,640,573 4,921,720 2,460,860 1,230,430 615,215 1,845,646 922,823 2,768,470 1,384,235 4,152,706 2,076,353 6,229,060 3,114,530 1,557,265 4,671,796 2,335,898 1,167,949 3,503,848 1,751,924

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