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Atlas › Integer Profiles › Node 42,576,100

42,576,100

22 × 52 × 72 × 8689
Abundant Even Composite

42,576,100 factors as 2^2 × 5^2 × 7^2 × 8689. Its 54 positive divisors give a proper-divisor sum of 64,910,510, so this integer is abundant. The Collatz stopping time is 191 steps.

Prime Factor Structure

Factorization String 2^2 × 5^2 × 7^2 × 8689
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 54
Divisor Sum (σ) 107,486,610
Proper Divisor Sum 64,910,510
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #42576077 ← → #42576101

Radix Representation

Decimal 42576100
Binary 10100010011010100011100100 (26 bits)
Octal 0o242324344
Hexadecimal 0x289A8E4

Divisor Catalog (54)

1 2 4 5 7 10 14 20 25 28 35 49 50 70 98 100 140 175 196 245 350 490 700 980 1,225 2,450 4,900 8,689 17,378 34,756 43,445 60,823 86,890 121,646 173,780 217,225 243,292 304,115 425,761 434,450 608,230 851,522 868,900 1,216,460 1,520,575 1,703,044 2,128,805 3,041,150 4,257,610 6,082,300 8,515,220 10,644,025 21,288,050 42,576,100

Collatz Trajectory (191 steps to reach 1)

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

42,576,100 21,288,050 10,644,025 31,932,076 15,966,038 7,983,019 23,949,058 11,974,529 35,923,588 17,961,794 8,980,897 26,942,692 13,471,346 6,735,673 20,207,020 10,103,510 5,051,755 15,155,266 7,577,633 22,732,900 11,366,450 5,683,225 17,049,676 8,524,838 4,262,419 12,787,258 6,393,629 19,180,888 9,590,444 4,795,222 2,397,611 7,192,834 3,596,417 10,789,252 5,394,626 2,697,313 8,091,940 4,045,970 2,022,985 6,068,956 3,034,478 1,517,239 4,551,718 2,275,859 6,827,578 3,413,789 10,241,368 5,120,684 2,560,342 1,280,171 3,840,514 1,920,257 5,760,772 2,880,386 1,440,193 4,320,580 2,160,290 1,080,145 3,240,436 1,620,218

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