7,829,084

2² × 67 × 131 × 223

Starting at 7,829,084, the Collatz iteration reaches 1 after 155 steps. The first transition is 3914542; the starting value is even with 24 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 67 × 131 × 223

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 14,074,368

Proper Divisor Sum 6,245,284

Digit Sum / Digital Root 38 (Root: 2)

Adjacent Primes #7829077 ← → #7829093

Radix Representation

Decimal	7829084
Binary	11101110111011001011100 (23 bits)
Octal	0o35673134
Hexadecimal	0x77765C

Divisor Catalog (24)

1 2 4 67 131 134 223 262 268 446 524 892 8,777 14,941 17,554 29,213 29,882 35,108 58,426 59,764 116,852 1,957,271 3,914,542 7,829,084

Collatz Trajectory (155 steps to reach 1)

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

7,829,084 3,914,542 1,957,271 5,871,814 2,935,907 8,807,722 4,403,861 13,211,584 6,605,792 3,302,896 1,651,448 825,724 412,862 206,431 619,294 309,647 928,942 464,471 1,393,414 696,707 2,090,122 1,045,061 3,135,184 1,567,592 783,796 391,898 195,949 587,848 293,924 146,962 73,481 220,444 110,222 55,111 165,334 82,667 248,002 124,001 372,004 186,002 93,001 279,004 139,502 69,751 209,254 104,627 313,882 156,941 470,824 235,412 117,706 58,853 176,560 88,280 44,140 22,070 11,035 33,106 16,553 49,660

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