8,202,720

2⁵ × 3 × 5 × 23 × 743

Starting at 8,202,720, the Collatz iteration reaches 1 after 106 steps. The first transition is 4101360; the starting value is even with 96 positive divisors.

Prime Factor Structure

Factorization String 2^5 × 3 × 5 × 23 × 743

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 26,998,272

Proper Divisor Sum 18,795,552

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #8202713 ← → #8202767

Radix Representation

Decimal	8202720
Binary	11111010010100111100000 (23 bits)
Octal	0o37224740
Hexadecimal	0x7D29E0

Divisor Catalog (60 of 96)

1 2 3 4 5 6 8 10 12 15 16 20 23 24 30 32 40 46 48 60 69 80 92 96 115 120 138 160 184 230 240 276 345 368 460 480 552 690 736 743 920 1,104 1,380 1,486 1,840 2,208 2,229 2,760 2,972 3,680 3,715 4,458 5,520 5,944 7,430 8,916 11,040 11,145 11,888 14,860

Collatz Trajectory (106 steps to reach 1)

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

8,202,720 4,101,360 2,050,680 1,025,340 512,670 256,335 769,006 384,503 1,153,510 576,755 1,730,266 865,133 2,595,400 1,297,700 648,850 324,425 973,276 486,638 243,319 729,958 364,979 1,094,938 547,469 1,642,408 821,204 410,602 205,301 615,904 307,952 153,976 76,988 38,494 19,247 57,742 28,871 86,614 43,307 129,922 64,961 194,884 97,442 48,721 146,164 73,082 36,541 109,624 54,812 27,406 13,703 41,110 20,555 61,666 30,833 92,500 46,250 23,125 69,376 34,688 17,344 8,672

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