2,760,520

2³ × 5 × 7 × 9859

Starting at 2,760,520, the Collatz iteration reaches 1 after 138 steps. The first transition is 1380260; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 5 × 7 × 9859

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 7,099,200

Proper Divisor Sum 4,338,680

Digit Sum / Digital Root 22 (Root: 4)

Adjacent Primes #2760509 ← → #2760521

Radix Representation

Decimal	2760520
Binary	1010100001111101001000 (22 bits)
Octal	0o12417510
Hexadecimal	0x2A1F48

Divisor Catalog (32)

1 2 4 5 7 8 10 14 20 28 35 40 56 70 140 280 9,859 19,718 39,436 49,295 69,013 78,872 98,590 138,026 197,180 276,052 345,065 394,360 552,104 690,130 1,380,260 2,760,520

Collatz Trajectory (138 steps to reach 1)

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

2,760,520 1,380,260 690,130 345,065 1,035,196 517,598 258,799 776,398 388,199 1,164,598 582,299 1,746,898 873,449 2,620,348 1,310,174 655,087 1,965,262 982,631 2,947,894 1,473,947 4,421,842 2,210,921 6,632,764 3,316,382 1,658,191 4,974,574 2,487,287 7,461,862 3,730,931 11,192,794 5,596,397 16,789,192 8,394,596 4,197,298 2,098,649 6,295,948 3,147,974 1,573,987 4,721,962 2,360,981 7,082,944 3,541,472 1,770,736 885,368 442,684 221,342 110,671 332,014 166,007 498,022 249,011 747,034 373,517 1,120,552 560,276 280,138 140,069 420,208 210,104 105,052

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