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Atlas › Integer Profiles › Node 42,226,100

42,226,100

22 × 52 × 7 × 179 × 337
Abundant Even Composite

42,226,100 factors as 2^2 × 5^2 × 7 × 179 × 337. Its 72 positive divisors give a proper-divisor sum of 63,392,140, so this integer is abundant. The Collatz stopping time is 328 steps.

Prime Factor Structure

Factorization String 2^2 × 5^2 × 7 × 179 × 337
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 105,618,240
Proper Divisor Sum 63,392,140
Digit Sum / Digital Root 17 (Root: 8)
Adjacent Primes #42226099 ← → #42226141

Radix Representation

Decimal 42226100
Binary 10100001000101000110110100 (26 bits)
Octal 0o241050664
Hexadecimal 0x28451B4

Divisor Catalog (60 of 72)

1 2 4 5 7 10 14 20 25 28 35 50 70 100 140 175 179 337 350 358 674 700 716 895 1,253 1,348 1,685 1,790 2,359 2,506 3,370 3,580 4,475 4,718 5,012 6,265 6,740 8,425 8,950 9,436 11,795 12,530 16,850 17,900 23,590 25,060 31,325 33,700 47,180 58,975 60,323 62,650 117,950 120,646 125,300 235,900 241,292 301,615 422,261 603,230

Collatz Trajectory (328 steps to reach 1)

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

42,226,100 21,113,050 10,556,525 31,669,576 15,834,788 7,917,394 3,958,697 11,876,092 5,938,046 2,969,023 8,907,070 4,453,535 13,360,606 6,680,303 20,040,910 10,020,455 30,061,366 15,030,683 45,092,050 22,546,025 67,638,076 33,819,038 16,909,519 50,728,558 25,364,279 76,092,838 38,046,419 114,139,258 57,069,629 171,208,888 85,604,444 42,802,222 21,401,111 64,203,334 32,101,667 96,305,002 48,152,501 144,457,504 72,228,752 36,114,376 18,057,188 9,028,594 4,514,297 13,542,892 6,771,446 3,385,723 10,157,170 5,078,585 15,235,756 7,617,878 3,808,939 11,426,818 5,713,409 17,140,228 8,570,114 4,285,057 12,855,172 6,427,586 3,213,793 9,641,380

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