7,582,644

2² × 3² × 347 × 607

Starting at 7,582,644, the Collatz iteration reaches 1 after 103 steps. The first transition is 3791322; the starting value is even with 36 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 347 × 607

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 19,254,144

Proper Divisor Sum 11,671,500

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7582613 ← → #7582649

Radix Representation

Decimal	7582644
Binary	11100111011001110110100 (23 bits)
Octal	0o34731664
Hexadecimal	0x73B3B4

Divisor Catalog (36)

1 2 3 4 6 9 12 18 36 347 607 694 1,041 1,214 1,388 1,821 2,082 2,428 3,123 3,642 4,164 5,463 6,246 7,284 10,926 12,492 21,852 210,629 421,258 631,887 842,516 1,263,774 1,895,661 2,527,548 3,791,322 7,582,644

Collatz Trajectory (103 steps to reach 1)

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

7,582,644 3,791,322 1,895,661 5,686,984 2,843,492 1,421,746 710,873 2,132,620 1,066,310 533,155 1,599,466 799,733 2,399,200 1,199,600 599,800 299,900 149,950 74,975 224,926 112,463 337,390 168,695 506,086 253,043 759,130 379,565 1,138,696 569,348 284,674 142,337 427,012 213,506 106,753 320,260 160,130 80,065 240,196 120,098 60,049 180,148 90,074 45,037 135,112 67,556 33,778 16,889 50,668 25,334 12,667 38,002 19,001 57,004 28,502 14,251 42,754 21,377 64,132 32,066 16,033 48,100

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