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Atlas › Integer Profiles › Node 48,367,278

48,367,278

2 × 32 × 17 × 263 × 601
Abundant Even Composite

48,367,278 factors as 2 × 3^2 × 17 × 263 × 601. Its 48 positive divisors give a proper-divisor sum of 63,200,178, so this integer is abundant. The Collatz stopping time is 199 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 17 × 263 × 601
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 111,567,456
Proper Divisor Sum 63,200,178
Digit Sum / Digital Root 45 (Root: 9)
Adjacent Primes #48367219 ← → #48367279

Radix Representation

Decimal 48367278
Binary 10111000100000011010101110 (26 bits)
Octal 0o270403256
Hexadecimal 0x2E206AE

Divisor Catalog (48)

1 2 3 6 9 17 18 34 51 102 153 263 306 526 601 789 1,202 1,578 1,803 2,367 3,606 4,471 4,734 5,409 8,942 10,217 10,818 13,413 20,434 26,826 30,651 40,239 61,302 80,478 91,953 158,063 183,906 316,126 474,189 948,378 1,422,567 2,687,071 2,845,134 5,374,142 8,061,213 16,122,426 24,183,639 48,367,278

Collatz Trajectory (199 steps to reach 1)

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

48,367,278 24,183,639 72,550,918 36,275,459 108,826,378 54,413,189 163,239,568 81,619,784 40,809,892 20,404,946 10,202,473 30,607,420 15,303,710 7,651,855 22,955,566 11,477,783 34,433,350 17,216,675 51,650,026 25,825,013 77,475,040 38,737,520 19,368,760 9,684,380 4,842,190 2,421,095 7,263,286 3,631,643 10,894,930 5,447,465 16,342,396 8,171,198 4,085,599 12,256,798 6,128,399 18,385,198 9,192,599 27,577,798 13,788,899 41,366,698 20,683,349 62,050,048 31,025,024 15,512,512 7,756,256 3,878,128 1,939,064 969,532 484,766 242,383 727,150 363,575 1,090,726 545,363 1,636,090 818,045 2,454,136 1,227,068 613,534 306,767

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