7,825,278

2 × 3 × 37 × 101 × 349

Starting at 7,825,278, the Collatz iteration reaches 1 after 155 steps. The first transition is 3912639; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 37 × 101 × 349

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 16,279,200

Proper Divisor Sum 8,453,922

Digit Sum / Digital Root 39 (Root: 3)

Adjacent Primes #7825261 ← → #7825327

Radix Representation

Decimal	7825278
Binary	11101110110011101111110 (23 bits)
Octal	0o35663576
Hexadecimal	0x77677E

Divisor Catalog (32)

1 2 3 6 37 74 101 111 202 222 303 349 606 698 1,047 2,094 3,737 7,474 11,211 12,913 22,422 25,826 35,249 38,739 70,498 77,478 105,747 211,494 1,304,213 2,608,426 3,912,639 7,825,278

Collatz Trajectory (155 steps to reach 1)

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

7,825,278 3,912,639 11,737,918 5,868,959 17,606,878 8,803,439 26,410,318 13,205,159 39,615,478 19,807,739 59,423,218 29,711,609 89,134,828 44,567,414 22,283,707 66,851,122 33,425,561 100,276,684 50,138,342 25,069,171 75,207,514 37,603,757 112,811,272 56,405,636 28,202,818 14,101,409 42,304,228 21,152,114 10,576,057 31,728,172 15,864,086 7,932,043 23,796,130 11,898,065 35,694,196 17,847,098 8,923,549 26,770,648 13,385,324 6,692,662 3,346,331 10,038,994 5,019,497 15,058,492 7,529,246 3,764,623 11,293,870 5,646,935 16,940,806 8,470,403 25,411,210 12,705,605 38,116,816 19,058,408 9,529,204 4,764,602 2,382,301 7,146,904 3,573,452 1,786,726

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