777,150

2 × 3² × 5² × 11 × 157

777,150 factors as 2 × 3^2 × 5^2 × 11 × 157. Its 72 positive divisors give a proper-divisor sum of 1,515,114, so this integer is abundant. The Collatz stopping time is 118 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 5^2 × 11 × 157

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 2,292,264

Proper Divisor Sum 1,515,114

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #777143 ← → #777151

Radix Representation

Decimal	777150
Binary	10111101101110111110 (20 bits)
Octal	0o2755676
Hexadecimal	0xBDBBE

Divisor Catalog (60 of 72)

1 2 3 5 6 9 10 11 15 18 22 25 30 33 45 50 55 66 75 90 99 110 150 157 165 198 225 275 314 330 450 471 495 550 785 825 942 990 1,413 1,570 1,650 1,727 2,355 2,475 2,826 3,454 3,925 4,710 4,950 5,181 7,065 7,850 8,635 10,362 11,775 14,130 15,543 17,270 23,550 25,905

Collatz Trajectory (118 steps to reach 1)

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

777,150 388,575 1,165,726 582,863 1,748,590 874,295 2,622,886 1,311,443 3,934,330 1,967,165 5,901,496 2,950,748 1,475,374 737,687 2,213,062 1,106,531 3,319,594 1,659,797 4,979,392 2,489,696 1,244,848 622,424 311,212 155,606 77,803 233,410 116,705 350,116 175,058 87,529 262,588 131,294 65,647 196,942 98,471 295,414 147,707 443,122 221,561 664,684 332,342 166,171 498,514 249,257 747,772 373,886 186,943 560,830 280,415 841,246 420,623 1,261,870 630,935 1,892,806 946,403 2,839,210 1,419,605 4,258,816 2,129,408 1,064,704

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