7,877,775

3 × 5² × 105037

Starting at 7,877,775, the Collatz iteration reaches 1 after 261 steps. The first transition is 23633326; the starting value is odd with 12 positive divisors.

Prime Factor Structure

Factorization String 3 × 5^2 × 105037

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 13,024,712

Proper Divisor Sum 5,146,937

Digit Sum / Digital Root 48 (Root: 3)

Adjacent Primes #7877773 ← → #7877777

Radix Representation

Decimal	7877775
Binary	11110000011010010001111 (23 bits)
Octal	0o36032217
Hexadecimal	0x78348F

Divisor Catalog (12)

1 3 5 15 25 75 105,037 315,111 525,185 1,575,555 2,625,925 7,877,775

Collatz Trajectory (261 steps to reach 1)

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

7,877,775 23,633,326 11,816,663 35,449,990 17,724,995 53,174,986 26,587,493 79,762,480 39,881,240 19,940,620 9,970,310 4,985,155 14,955,466 7,477,733 22,433,200 11,216,600 5,608,300 2,804,150 1,402,075 4,206,226 2,103,113 6,309,340 3,154,670 1,577,335 4,732,006 2,366,003 7,098,010 3,549,005 10,647,016 5,323,508 2,661,754 1,330,877 3,992,632 1,996,316 998,158 499,079 1,497,238 748,619 2,245,858 1,122,929 3,368,788 1,684,394 842,197 2,526,592 1,263,296 631,648 315,824 157,912 78,956 39,478 19,739 59,218 29,609 88,828 44,414 22,207 66,622 33,311 99,934 49,967

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