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Atlas › Integer Profiles › Node 6,961,968

6,961,968

24 × 32 × 13 × 3719
Abundant Even Composite

6,961,968 factors as 2^4 × 3^2 × 13 × 3719. Its 60 positive divisors give a proper-divisor sum of 14,026,272, so this integer is abundant. The Collatz stopping time is 129 steps.

Prime Factor Structure

Factorization String 2^4 × 3^2 × 13 × 3719
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 60
Divisor Sum (σ) 20,988,240
Proper Divisor Sum 14,026,272
Digit Sum / Digital Root 45 (Root: 9)
Adjacent Primes #6961967 ← → #6961979

Radix Representation

Decimal 6961968
Binary 11010100011101100110000 (23 bits)
Octal 0o32435460
Hexadecimal 0x6A3B30

Divisor Catalog (60)

1 2 3 4 6 8 9 12 13 16 18 24 26 36 39 48 52 72 78 104 117 144 156 208 234 312 468 624 936 1,872 3,719 7,438 11,157 14,876 22,314 29,752 33,471 44,628 48,347 59,504 66,942 89,256 96,694 133,884 145,041 178,512 193,388 267,768 290,082 386,776 435,123 535,536 580,164 773,552 870,246 1,160,328 1,740,492 2,320,656 3,480,984 6,961,968

Collatz Trajectory (129 steps to reach 1)

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

6,961,968 3,480,984 1,740,492 870,246 435,123 1,305,370 652,685 1,958,056 979,028 489,514 244,757 734,272 367,136 183,568 91,784 45,892 22,946 11,473 34,420 17,210 8,605 25,816 12,908 6,454 3,227 9,682 4,841 14,524 7,262 3,631 10,894 5,447 16,342 8,171 24,514 12,257 36,772 18,386 9,193 27,580 13,790 6,895 20,686 10,343 31,030 15,515 46,546 23,273 69,820 34,910 17,455 52,366 26,183 78,550 39,275 117,826 58,913 176,740 88,370 44,185

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