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Atlas › Integer Profiles › Node 42,469,840

42,469,840

24 × 5 × 7 × 181 × 419
Abundant Even Composite

42,469,840 factors as 2^4 × 5 × 7 × 181 × 419. Its 80 positive divisors give a proper-divisor sum of 71,272,880, so this integer is abundant. The Collatz stopping time is 129 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 7 × 181 × 419
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 113,742,720
Proper Divisor Sum 71,272,880
Digit Sum / Digital Root 37 (Root: 1)
Adjacent Primes #42469837 ← → #42469841

Radix Representation

Decimal 42469840
Binary 10100010000000100111010000 (26 bits)
Octal 0o242004720
Hexadecimal 0x28809D0

Divisor Catalog (60 of 80)

1 2 4 5 7 8 10 14 16 20 28 35 40 56 70 80 112 140 181 280 362 419 560 724 838 905 1,267 1,448 1,676 1,810 2,095 2,534 2,896 2,933 3,352 3,620 4,190 5,068 5,866 6,335 6,704 7,240 8,380 10,136 11,732 12,670 14,480 14,665 16,760 20,272 23,464 25,340 29,330 33,520 46,928 50,680 58,660 75,839 101,360 117,320

Collatz Trajectory (129 steps to reach 1)

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

42,469,840 21,234,920 10,617,460 5,308,730 2,654,365 7,963,096 3,981,548 1,990,774 995,387 2,986,162 1,493,081 4,479,244 2,239,622 1,119,811 3,359,434 1,679,717 5,039,152 2,519,576 1,259,788 629,894 314,947 944,842 472,421 1,417,264 708,632 354,316 177,158 88,579 265,738 132,869 398,608 199,304 99,652 49,826 24,913 74,740 37,370 18,685 56,056 28,028 14,014 7,007 21,022 10,511 31,534 15,767 47,302 23,651 70,954 35,477 106,432 53,216 26,608 13,304 6,652 3,326 1,663 4,990 2,495 7,486

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