772,863

3 × 7 × 13 × 19 × 149

772,863 factors as 3 × 7 × 13 × 19 × 149. Its 32 positive divisors give a proper-divisor sum of 571,137, so this integer is deficient. The Collatz stopping time is 100 steps.

Prime Factor Structure

Factorization String 3 × 7 × 13 × 19 × 149

Distinct Prime Factors 5

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 1,344,000

Proper Divisor Sum 571,137

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #772859 ← → #772867

Radix Representation

Decimal	772863
Binary	10111100101011111111 (20 bits)
Octal	0o2745377
Hexadecimal	0xBCAFF

Divisor Catalog (32)

Collatz Trajectory (100 steps to reach 1)

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

772,863 2,318,590 1,159,295 3,477,886 1,738,943 5,216,830 2,608,415 7,825,246 3,912,623 11,737,870 5,868,935 17,606,806 8,803,403 26,410,210 13,205,105 39,615,316 19,807,658 9,903,829 29,711,488 14,855,744 7,427,872 3,713,936 1,856,968 928,484 464,242 232,121 696,364 348,182 174,091 522,274 261,137 783,412 391,706 195,853 587,560 293,780 146,890 73,445 220,336 110,168 55,084 27,542 13,771 41,314 20,657 61,972 30,986 15,493 46,480 23,240 11,620 5,810 2,905 8,716 4,358 2,179 6,538 3,269 9,808 4,904

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