7,968,480

2⁵ × 3 × 5 × 13 × 1277

Starting at 7,968,480, the Collatz iteration reaches 1 after 93 steps. The first transition is 3984240; the starting value is even with 96 positive divisors.

Prime Factor Structure

Factorization String 2^5 × 3 × 5 × 13 × 1277

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 27,052,704

Proper Divisor Sum 19,084,224

Digit Sum / Digital Root 42 (Root: 6)

Adjacent Primes #7968479 ← → #7968487

Radix Representation

Decimal	7968480
Binary	11110011001011011100000 (23 bits)
Octal	0o36313340
Hexadecimal	0x7996E0

Divisor Catalog (60 of 96)

1 2 3 4 5 6 8 10 12 13 15 16 20 24 26 30 32 39 40 48 52 60 65 78 80 96 104 120 130 156 160 195 208 240 260 312 390 416 480 520 624 780 1,040 1,248 1,277 1,560 2,080 2,554 3,120 3,831 5,108 6,240 6,385 7,662 10,216 12,770 15,324 16,601 19,155 20,432

Collatz Trajectory (93 steps to reach 1)

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

7,968,480 3,984,240 1,992,120 996,060 498,030 249,015 747,046 373,523 1,120,570 560,285 1,680,856 840,428 420,214 210,107 630,322 315,161 945,484 472,742 236,371 709,114 354,557 1,063,672 531,836 265,918 132,959 398,878 199,439 598,318 299,159 897,478 448,739 1,346,218 673,109 2,019,328 1,009,664 504,832 252,416 126,208 63,104 31,552 15,776 7,888 3,944 1,972 986 493 1,480 740 370 185 556 278 139 418 209 628 314 157 472 236

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