λ
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Atlas › Integer Profiles › Node 77,519,344

77,519,344

24 × 7 × 31 × 83 × 269
Abundant Even Composite

77,519,344 factors as 2^4 × 7 × 31 × 83 × 269. Its 80 positive divisors give a proper-divisor sum of 102,469,136, so this integer is abundant. The Collatz stopping time is 135 steps.

Prime Factor Structure

Factorization String 2^4 × 7 × 31 × 83 × 269
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 179,988,480
Proper Divisor Sum 102,469,136
Digit Sum / Digital Root 40 (Root: 4)
Adjacent Primes #77519341 ← → #77519347

Radix Representation

Decimal 77519344
Binary 100100111101101100111110000 (27 bits)
Octal 0o447554760
Hexadecimal 0x49ED9F0

Divisor Catalog (60 of 80)

1 2 4 7 8 14 16 28 31 56 62 83 112 124 166 217 248 269 332 434 496 538 581 664 868 1,076 1,162 1,328 1,736 1,883 2,152 2,324 2,573 3,472 3,766 4,304 4,648 5,146 7,532 8,339 9,296 10,292 15,064 16,678 18,011 20,584 22,327 30,128 33,356 36,022 41,168 44,654 58,373 66,712 72,044 89,308 116,746 133,424 144,088 156,289

Collatz Trajectory (135 steps to reach 1)

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

77,519,344 38,759,672 19,379,836 9,689,918 4,844,959 14,534,878 7,267,439 21,802,318 10,901,159 32,703,478 16,351,739 49,055,218 24,527,609 73,582,828 36,791,414 18,395,707 55,187,122 27,593,561 82,780,684 41,390,342 20,695,171 62,085,514 31,042,757 93,128,272 46,564,136 23,282,068 11,641,034 5,820,517 17,461,552 8,730,776 4,365,388 2,182,694 1,091,347 3,274,042 1,637,021 4,911,064 2,455,532 1,227,766 613,883 1,841,650 920,825 2,762,476 1,381,238 690,619 2,071,858 1,035,929 3,107,788 1,553,894 776,947 2,330,842 1,165,421 3,496,264 1,748,132 874,066 437,033 1,311,100 655,550 327,775 983,326 491,663

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