7,633,100

2² × 5² × 37 × 2063

Starting at 7,633,100, the Collatz iteration reaches 1 after 155 steps. The first transition is 3816550; the starting value is even with 36 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 5^2 × 37 × 2063

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 17,019,744

Proper Divisor Sum 9,386,644

Digit Sum / Digital Root 20 (Root: 2)

Adjacent Primes #7633091 ← → #7633103

Radix Representation

Decimal	7633100
Binary	11101000111100011001100 (23 bits)
Octal	0o35074314
Hexadecimal	0x7478CC

Divisor Catalog (36)

1 2 4 5 10 20 25 37 50 74 100 148 185 370 740 925 1,850 2,063 3,700 4,126 8,252 10,315 20,630 41,260 51,575 76,331 103,150 152,662 206,300 305,324 381,655 763,310 1,526,620 1,908,275 3,816,550 7,633,100

Collatz Trajectory (155 steps to reach 1)

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

7,633,100 3,816,550 1,908,275 5,724,826 2,862,413 8,587,240 4,293,620 2,146,810 1,073,405 3,220,216 1,610,108 805,054 402,527 1,207,582 603,791 1,811,374 905,687 2,717,062 1,358,531 4,075,594 2,037,797 6,113,392 3,056,696 1,528,348 764,174 382,087 1,146,262 573,131 1,719,394 859,697 2,579,092 1,289,546 644,773 1,934,320 967,160 483,580 241,790 120,895 362,686 181,343 544,030 272,015 816,046 408,023 1,224,070 612,035 1,836,106 918,053 2,754,160 1,377,080 688,540 344,270 172,135 516,406 258,203 774,610 387,305 1,161,916 580,958 290,479

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