223,626

2 × 3 × 13 × 47 × 61

Starting at 223,626, the Collatz iteration reaches 1 after 93 steps. The first transition is 111813; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 13 × 47 × 61

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 499,968

Proper Divisor Sum 276,342

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #223621 ← → #223633

Radix Representation

Decimal	223626
Binary	110110100110001010 (18 bits)
Octal	0o664612
Hexadecimal	0x3698A

Divisor Catalog (32)

1 2 3 6 13 26 39 47 61 78 94 122 141 183 282 366 611 793 1,222 1,586 1,833 2,379 2,867 3,666 4,758 5,734 8,601 17,202 37,271 74,542 111,813 223,626

Collatz Trajectory (93 steps to reach 1)

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

223,626 111,813 335,440 167,720 83,860 41,930 20,965 62,896 31,448 15,724 7,862 3,931 11,794 5,897 17,692 8,846 4,423 13,270 6,635 19,906 9,953 29,860 14,930 7,465 22,396 11,198 5,599 16,798 8,399 25,198 12,599 37,798 18,899 56,698 28,349 85,048 42,524 21,262 10,631 31,894 15,947 47,842 23,921 71,764 35,882 17,941 53,824 26,912 13,456 6,728 3,364 1,682 841 2,524 1,262 631 1,894 947 2,842 1,421

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