7,762,248

2³ × 3² × 13 × 8293

Starting at 7,762,248, the Collatz iteration reaches 1 after 217 steps. The first transition is 3881124; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 13 × 8293

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 22,642,620

Proper Divisor Sum 14,880,372

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7762229 ← → #7762259

Radix Representation

Decimal	7762248
Binary	11101100111000101001000 (23 bits)
Octal	0o35470510
Hexadecimal	0x767148

Divisor Catalog (48)

1 2 3 4 6 8 9 12 13 18 24 26 36 39 52 72 78 104 117 156 234 312 468 936 8,293 16,586 24,879 33,172 49,758 66,344 74,637 99,516 107,809 149,274 199,032 215,618 298,548 323,427 431,236 597,096 646,854 862,472 970,281 1,293,708 1,940,562 2,587,416 3,881,124 7,762,248

Collatz Trajectory (217 steps to reach 1)

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

7,762,248 3,881,124 1,940,562 970,281 2,910,844 1,455,422 727,711 2,183,134 1,091,567 3,274,702 1,637,351 4,912,054 2,456,027 7,368,082 3,684,041 11,052,124 5,526,062 2,763,031 8,289,094 4,144,547 12,433,642 6,216,821 18,650,464 9,325,232 4,662,616 2,331,308 1,165,654 582,827 1,748,482 874,241 2,622,724 1,311,362 655,681 1,967,044 983,522 491,761 1,475,284 737,642 368,821 1,106,464 553,232 276,616 138,308 69,154 34,577 103,732 51,866 25,933 77,800 38,900 19,450 9,725 29,176 14,588 7,294 3,647 10,942 5,471 16,414 8,207

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