λ
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Atlas › Integer Profiles › Node 55,646,080

55,646,080

27 × 5 × 7 × 12421
Abundant Even Composite

55,646,080 factors as 2^7 × 5 × 7 × 12421. Its 64 positive divisors give a proper-divisor sum of 96,399,200, so this integer is abundant. The Collatz stopping time is 101 steps.

Prime Factor Structure

Factorization String 2^7 × 5 × 7 × 12421
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 152,045,280
Proper Divisor Sum 96,399,200
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #55646069 ← → #55646089

Radix Representation

Decimal 55646080
Binary 11010100010001011110000000 (26 bits)
Octal 0o324213600
Hexadecimal 0x3511780

Divisor Catalog (60 of 64)

1 2 4 5 7 8 10 14 16 20 28 32 35 40 56 64 70 80 112 128 140 160 224 280 320 448 560 640 896 1,120 2,240 4,480 12,421 24,842 49,684 62,105 86,947 99,368 124,210 173,894 198,736 248,420 347,788 397,472 434,735 496,840 695,576 794,944 869,470 993,680 1,391,152 1,589,888 1,738,940 1,987,360 2,782,304 3,477,880 3,974,720 5,564,608 6,955,760 7,949,440

Collatz Trajectory (101 steps to reach 1)

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

55,646,080 27,823,040 13,911,520 6,955,760 3,477,880 1,738,940 869,470 434,735 1,304,206 652,103 1,956,310 978,155 2,934,466 1,467,233 4,401,700 2,200,850 1,100,425 3,301,276 1,650,638 825,319 2,475,958 1,237,979 3,713,938 1,856,969 5,570,908 2,785,454 1,392,727 4,178,182 2,089,091 6,267,274 3,133,637 9,400,912 4,700,456 2,350,228 1,175,114 587,557 1,762,672 881,336 440,668 220,334 110,167 330,502 165,251 495,754 247,877 743,632 371,816 185,908 92,954 46,477 139,432 69,716 34,858 17,429 52,288 26,144 13,072 6,536 3,268 1,634

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