7,415,408

2⁴ × 7 × 11 × 13 × 463

Starting at 7,415,408, the Collatz iteration reaches 1 after 235 steps. The first transition is 3707704; the starting value is even with 80 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 7 × 11 × 13 × 463

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 19,332,096

Proper Divisor Sum 11,916,688

Digit Sum / Digital Root 29 (Root: 2)

Adjacent Primes #7415371 ← → #7415423

Radix Representation

Decimal	7415408
Binary	11100010010011001110000 (23 bits)
Octal	0o34223160
Hexadecimal	0x712670

Divisor Catalog (60 of 80)

1 2 4 7 8 11 13 14 16 22 26 28 44 52 56 77 88 91 104 112 143 154 176 182 208 286 308 364 463 572 616 728 926 1,001 1,144 1,232 1,456 1,852 2,002 2,288 3,241 3,704 4,004 5,093 6,019 6,482 7,408 8,008 10,186 12,038 12,964 16,016 20,372 24,076 25,928 35,651 40,744 42,133 48,152 51,856

Collatz Trajectory (235 steps to reach 1)

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

7,415,408 3,707,704 1,853,852 926,926 463,463 1,390,390 695,195 2,085,586 1,042,793 3,128,380 1,564,190 782,095 2,346,286 1,173,143 3,519,430 1,759,715 5,279,146 2,639,573 7,918,720 3,959,360 1,979,680 989,840 494,920 247,460 123,730 61,865 185,596 92,798 46,399 139,198 69,599 208,798 104,399 313,198 156,599 469,798 234,899 704,698 352,349 1,057,048 528,524 264,262 132,131 396,394 198,197 594,592 297,296 148,648 74,324 37,162 18,581 55,744 27,872 13,936 6,968 3,484 1,742 871 2,614 1,307

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