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Atlas › Integer Profiles › Node 48,359,752

48,359,752

23 × 7 × 31 × 89 × 313
Abundant Even Composite

48,359,752 factors as 2^3 × 7 × 31 × 89 × 313. Its 64 positive divisors give a proper-divisor sum of 60,158,648, so this integer is abundant. The Collatz stopping time is 217 steps.

Prime Factor Structure

Factorization String 2^3 × 7 × 31 × 89 × 313
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 108,518,400
Proper Divisor Sum 60,158,648
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #48359719 ← → #48359789

Radix Representation

Decimal 48359752
Binary 10111000011110100101001000 (26 bits)
Octal 0o270364510
Hexadecimal 0x2E1E948

Divisor Catalog (60 of 64)

1 2 4 7 8 14 28 31 56 62 89 124 178 217 248 313 356 434 623 626 712 868 1,246 1,252 1,736 2,191 2,492 2,504 2,759 4,382 4,984 5,518 8,764 9,703 11,036 17,528 19,313 19,406 22,072 27,857 38,626 38,812 55,714 67,921 77,252 77,624 111,428 135,842 154,504 194,999 222,856 271,684 389,998 543,368 779,996 863,567 1,559,992 1,727,134 3,454,268 6,044,969

Collatz Trajectory (217 steps to reach 1)

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

48,359,752 24,179,876 12,089,938 6,044,969 18,134,908 9,067,454 4,533,727 13,601,182 6,800,591 20,401,774 10,200,887 30,602,662 15,301,331 45,903,994 22,951,997 68,855,992 34,427,996 17,213,998 8,606,999 25,820,998 12,910,499 38,731,498 19,365,749 58,097,248 29,048,624 14,524,312 7,262,156 3,631,078 1,815,539 5,446,618 2,723,309 8,169,928 4,084,964 2,042,482 1,021,241 3,063,724 1,531,862 765,931 2,297,794 1,148,897 3,446,692 1,723,346 861,673 2,585,020 1,292,510 646,255 1,938,766 969,383 2,908,150 1,454,075 4,362,226 2,181,113 6,543,340 3,271,670 1,635,835 4,907,506 2,453,753 7,361,260 3,680,630 1,840,315

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