782,761

7 × 67 × 1669

Starting at 782,761, the Collatz iteration reaches 1 after 100 steps. The first transition is 2348284; the starting value is odd with 8 positive divisors.

Prime Factor Structure

Factorization String 7 × 67 × 1669

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 908,480

Proper Divisor Sum 125,719

Digit Sum / Digital Root 31 (Root: 4)

Adjacent Primes #782723 ← → #782777

Radix Representation

Decimal	782761
Binary	10111111000110101001 (20 bits)
Octal	0o2770651
Hexadecimal	0xBF1A9

Divisor Catalog (8)

1 7 67 469 1,669 11,683 111,823 782,761

Collatz Trajectory (100 steps to reach 1)

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

782,761 2,348,284 1,174,142 587,071 1,761,214 880,607 2,641,822 1,320,911 3,962,734 1,981,367 5,944,102 2,972,051 8,916,154 4,458,077 13,374,232 6,687,116 3,343,558 1,671,779 5,015,338 2,507,669 7,523,008 3,761,504 1,880,752 940,376 470,188 235,094 117,547 352,642 176,321 528,964 264,482 132,241 396,724 198,362 99,181 297,544 148,772 74,386 37,193 111,580 55,790 27,895 83,686 41,843 125,530 62,765 188,296 94,148 47,074 23,537 70,612 35,306 17,653 52,960 26,480 13,240 6,620 3,310 1,655 4,966

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