λ
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7,833,560

23 × 5 × 7 × 101 × 277
Abundant Even Composite

7,833,560 factors as 2^3 × 5 × 7 × 101 × 277. Its 64 positive divisors give a proper-divisor sum of 12,582,760, so this integer is abundant. The Collatz stopping time is 217 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 7 × 101 × 277
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 20,416,320
Proper Divisor Sum 12,582,760
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #7833517 ← → #7833563

Radix Representation

Decimal 7833560
Binary 11101111000011111011000 (23 bits)
Octal 0o35703730
Hexadecimal 0x7787D8

Divisor Catalog (60 of 64)

1 2 4 5 7 8 10 14 20 28 35 40 56 70 101 140 202 277 280 404 505 554 707 808 1,010 1,108 1,385 1,414 1,939 2,020 2,216 2,770 2,828 3,535 3,878 4,040 5,540 5,656 7,070 7,756 9,695 11,080 14,140 15,512 19,390 27,977 28,280 38,780 55,954 77,560 111,908 139,885 195,839 223,816 279,770 391,678 559,540 783,356 979,195 1,119,080

Collatz Trajectory (217 steps to reach 1)

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

7,833,560 3,916,780 1,958,390 979,195 2,937,586 1,468,793 4,406,380 2,203,190 1,101,595 3,304,786 1,652,393 4,957,180 2,478,590 1,239,295 3,717,886 1,858,943 5,576,830 2,788,415 8,365,246 4,182,623 12,547,870 6,273,935 18,821,806 9,410,903 28,232,710 14,116,355 42,349,066 21,174,533 63,523,600 31,761,800 15,880,900 7,940,450 3,970,225 11,910,676 5,955,338 2,977,669 8,933,008 4,466,504 2,233,252 1,116,626 558,313 1,674,940 837,470 418,735 1,256,206 628,103 1,884,310 942,155 2,826,466 1,413,233 4,239,700 2,119,850 1,059,925 3,179,776 1,589,888 794,944 397,472 198,736 99,368 49,684

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