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Atlas › Integer Profiles › Node 7,835,232

7,835,232

25 × 3 × 17 × 4801
Abundant Even Composite

7,835,232 factors as 2^5 × 3 × 17 × 4801. Its 48 positive divisors give a proper-divisor sum of 13,946,640, so this integer is abundant. The Collatz stopping time is 93 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 17 × 4801
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 21,781,872
Proper Divisor Sum 13,946,640
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #7835209 ← → #7835251

Radix Representation

Decimal 7835232
Binary 11101111000111001100000 (23 bits)
Octal 0o35707140
Hexadecimal 0x778E60

Divisor Catalog (48)

1 2 3 4 6 8 12 16 17 24 32 34 48 51 68 96 102 136 204 272 408 544 816 1,632 4,801 9,602 14,403 19,204 28,806 38,408 57,612 76,816 81,617 115,224 153,632 163,234 230,448 244,851 326,468 460,896 489,702 652,936 979,404 1,305,872 1,958,808 2,611,744 3,917,616 7,835,232

Collatz Trajectory (93 steps to reach 1)

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

7,835,232 3,917,616 1,958,808 979,404 489,702 244,851 734,554 367,277 1,101,832 550,916 275,458 137,729 413,188 206,594 103,297 309,892 154,946 77,473 232,420 116,210 58,105 174,316 87,158 43,579 130,738 65,369 196,108 98,054 49,027 147,082 73,541 220,624 110,312 55,156 27,578 13,789 41,368 20,684 10,342 5,171 15,514 7,757 23,272 11,636 5,818 2,909 8,728 4,364 2,182 1,091 3,274 1,637 4,912 2,456 1,228 614 307 922 461 1,384

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