7,854,960

2⁴ × 3 × 5 × 23 × 1423

Starting at 7,854,960, the Collatz iteration reaches 1 after 186 steps. The first transition is 3927480; the starting value is even with 80 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 3 × 5 × 23 × 1423

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 25,426,944

Proper Divisor Sum 17,571,984

Digit Sum / Digital Root 39 (Root: 3)

Adjacent Primes #7854953 ← → #7854967

Radix Representation

Decimal	7854960
Binary	11101111101101101110000 (23 bits)
Octal	0o35755560
Hexadecimal	0x77DB70

Divisor Catalog (60 of 80)

1 2 3 4 5 6 8 10 12 15 16 20 23 24 30 40 46 48 60 69 80 92 115 120 138 184 230 240 276 345 368 460 552 690 920 1,104 1,380 1,423 1,840 2,760 2,846 4,269 5,520 5,692 7,115 8,538 11,384 14,230 17,076 21,345 22,768 28,460 32,729 34,152 42,690 56,920 65,458 68,304 85,380 98,187

Collatz Trajectory (186 steps to reach 1)

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

7,854,960 3,927,480 1,963,740 981,870 490,935 1,472,806 736,403 2,209,210 1,104,605 3,313,816 1,656,908 828,454 414,227 1,242,682 621,341 1,864,024 932,012 466,006 233,003 699,010 349,505 1,048,516 524,258 262,129 786,388 393,194 196,597 589,792 294,896 147,448 73,724 36,862 18,431 55,294 27,647 82,942 41,471 124,414 62,207 186,622 93,311 279,934 139,967 419,902 209,951 629,854 314,927 944,782 472,391 1,417,174 708,587 2,125,762 1,062,881 3,188,644 1,594,322 797,161 2,391,484 1,195,742 597,871 1,793,614

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