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Atlas › Integer Profiles › Node 8,209,180

8,209,180

22 × 5 × 7 × 191 × 307
Abundant Even Composite

8,209,180 factors as 2^2 × 5 × 7 × 191 × 307. Its 48 positive divisors give a proper-divisor sum of 11,660,516, so this integer is abundant. The Collatz stopping time is 106 steps.

Prime Factor Structure

Factorization String 2^2 × 5 × 7 × 191 × 307
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 19,869,696
Proper Divisor Sum 11,660,516
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #8209171 ← → #8209193

Radix Representation

Decimal 8209180
Binary 11111010100001100011100 (23 bits)
Octal 0o37241434
Hexadecimal 0x7D431C

Divisor Catalog (48)

1 2 4 5 7 10 14 20 28 35 70 140 191 307 382 614 764 955 1,228 1,337 1,535 1,910 2,149 2,674 3,070 3,820 4,298 5,348 6,140 6,685 8,596 10,745 13,370 21,490 26,740 42,980 58,637 117,274 234,548 293,185 410,459 586,370 820,918 1,172,740 1,641,836 2,052,295 4,104,590 8,209,180

Collatz Trajectory (106 steps to reach 1)

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

8,209,180 4,104,590 2,052,295 6,156,886 3,078,443 9,235,330 4,617,665 13,852,996 6,926,498 3,463,249 10,389,748 5,194,874 2,597,437 7,792,312 3,896,156 1,948,078 974,039 2,922,118 1,461,059 4,383,178 2,191,589 6,574,768 3,287,384 1,643,692 821,846 410,923 1,232,770 616,385 1,849,156 924,578 462,289 1,386,868 693,434 346,717 1,040,152 520,076 260,038 130,019 390,058 195,029 585,088 292,544 146,272 73,136 36,568 18,284 9,142 4,571 13,714 6,857 20,572 10,286 5,143 15,430 7,715 23,146 11,573 34,720 17,360 8,680

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