7,825,414

2 × 89 × 43963

Starting at 7,825,414, the Collatz iteration reaches 1 after 217 steps. The first transition is 3912707; the starting value is even with 8 positive divisors.

Prime Factor Structure

Factorization String 2 × 89 × 43963

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 8

Divisor Sum (σ) 11,870,280

Proper Divisor Sum 4,044,866

Digit Sum / Digital Root 31 (Root: 4)

Adjacent Primes #7825409 ← → #7825417

Radix Representation

Decimal	7825414
Binary	11101110110100000000110 (23 bits)
Octal	0o35664006
Hexadecimal	0x776806

Divisor Catalog (8)

1 2 89 178 43,963 87,926 3,912,707 7,825,414

Collatz Trajectory (217 steps to reach 1)

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

7,825,414 3,912,707 11,738,122 5,869,061 17,607,184 8,803,592 4,401,796 2,200,898 1,100,449 3,301,348 1,650,674 825,337 2,476,012 1,238,006 619,003 1,857,010 928,505 2,785,516 1,392,758 696,379 2,089,138 1,044,569 3,133,708 1,566,854 783,427 2,350,282 1,175,141 3,525,424 1,762,712 881,356 440,678 220,339 661,018 330,509 991,528 495,764 247,882 123,941 371,824 185,912 92,956 46,478 23,239 69,718 34,859 104,578 52,289 156,868 78,434 39,217 117,652 58,826 29,413 88,240 44,120 22,060 11,030 5,515 16,546 8,273

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