3,672,840

2³ × 3 × 5 × 127 × 241

Starting at 3,672,840, the Collatz iteration reaches 1 after 203 steps. The first transition is 1836420; the starting value is even with 64 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 127 × 241

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 11,151,360

Proper Divisor Sum 7,478,520

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #3672829 ← → #3672853

Radix Representation

Decimal	3672840
Binary	1110000000101100001000 (22 bits)
Octal	0o16005410
Hexadecimal	0x380B08

Divisor Catalog (60 of 64)

1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 127 241 254 381 482 508 635 723 762 964 1,016 1,205 1,270 1,446 1,524 1,905 1,928 2,410 2,540 2,892 3,048 3,615 3,810 4,820 5,080 5,784 7,230 7,620 9,640 14,460 15,240 28,920 30,607 61,214 91,821 122,428 153,035 183,642 244,856 306,070 367,284 459,105 612,140 734,568

Collatz Trajectory (203 steps to reach 1)

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

3,672,840 1,836,420 918,210 459,105 1,377,316 688,658 344,329 1,032,988 516,494 258,247 774,742 387,371 1,162,114 581,057 1,743,172 871,586 435,793 1,307,380 653,690 326,845 980,536 490,268 245,134 122,567 367,702 183,851 551,554 275,777 827,332 413,666 206,833 620,500 310,250 155,125 465,376 232,688 116,344 58,172 29,086 14,543 43,630 21,815 65,446 32,723 98,170 49,085 147,256 73,628 36,814 18,407 55,222 27,611 82,834 41,417 124,252 62,126 31,063 93,190 46,595 139,786

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