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Atlas › Integer Profiles › Node 77,279,752

77,279,752

23 × 11 × 41 × 21419
Abundant Even Composite

77,279,752 factors as 2^3 × 11 × 41 × 21419. Its 32 positive divisors give a proper-divisor sum of 84,655,448, so this integer is abundant. The Collatz stopping time is 122 steps.

Prime Factor Structure

Factorization String 2^3 × 11 × 41 × 21419
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 161,935,200
Proper Divisor Sum 84,655,448
Digit Sum / Digital Root 46 (Root: 1)
Adjacent Primes #77279749 ← → #77279753

Radix Representation

Decimal 77279752
Binary 100100110110011001000001000 (27 bits)
Octal 0o446631010
Hexadecimal 0x49B3208

Divisor Catalog (32)

1 2 4 8 11 22 41 44 82 88 164 328 451 902 1,804 3,608 21,419 42,838 85,676 171,352 235,609 471,218 878,179 942,436 1,756,358 1,884,872 3,512,716 7,025,432 9,659,969 19,319,938 38,639,876 77,279,752

Collatz Trajectory (122 steps to reach 1)

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

77,279,752 38,639,876 19,319,938 9,659,969 28,979,908 14,489,954 7,244,977 21,734,932 10,867,466 5,433,733 16,301,200 8,150,600 4,075,300 2,037,650 1,018,825 3,056,476 1,528,238 764,119 2,292,358 1,146,179 3,438,538 1,719,269 5,157,808 2,578,904 1,289,452 644,726 322,363 967,090 483,545 1,450,636 725,318 362,659 1,087,978 543,989 1,631,968 815,984 407,992 203,996 101,998 50,999 152,998 76,499 229,498 114,749 344,248 172,124 86,062 43,031 129,094 64,547 193,642 96,821 290,464 145,232 72,616 36,308 18,154 9,077 27,232 13,616

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