8,420,220

2² × 3³ × 5 × 31 × 503

8,420,220 factors as 2^2 × 3^3 × 5 × 31 × 503. Its 96 positive divisors give a proper-divisor sum of 18,674,820, so this integer is abundant. The Collatz stopping time is 199 steps.

Prime Factor Structure

Factorization String 2^2 × 3^3 × 5 × 31 × 503

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 27,095,040

Proper Divisor Sum 18,674,820

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #8420207 ← → #8420221

Radix Representation

Decimal	8420220
Binary	100000000111101101111100 (24 bits)
Octal	0o40075574
Hexadecimal	0x807B7C

Divisor Catalog (60 of 96)

1 2 3 4 5 6 9 10 12 15 18 20 27 30 31 36 45 54 60 62 90 93 108 124 135 155 180 186 270 279 310 372 465 503 540 558 620 837 930 1,006 1,116 1,395 1,509 1,674 1,860 2,012 2,515 2,790 3,018 3,348 4,185 4,527 5,030 5,580 6,036 7,545 8,370 9,054 10,060 13,581

Collatz Trajectory (199 steps to reach 1)

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

8,420,220 4,210,110 2,105,055 6,315,166 3,157,583 9,472,750 4,736,375 14,209,126 7,104,563 21,313,690 10,656,845 31,970,536 15,985,268 7,992,634 3,996,317 11,988,952 5,994,476 2,997,238 1,498,619 4,495,858 2,247,929 6,743,788 3,371,894 1,685,947 5,057,842 2,528,921 7,586,764 3,793,382 1,896,691 5,690,074 2,845,037 8,535,112 4,267,556 2,133,778 1,066,889 3,200,668 1,600,334 800,167 2,400,502 1,200,251 3,600,754 1,800,377 5,401,132 2,700,566 1,350,283 4,050,850 2,025,425 6,076,276 3,038,138 1,519,069 4,557,208 2,278,604 1,139,302 569,651 1,708,954 854,477 2,563,432 1,281,716 640,858 320,429

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