7,648,160

2⁵ × 5 × 13 × 3677

7,648,160 factors as 2^5 × 5 × 13 × 3677. Its 48 positive divisors give a proper-divisor sum of 11,815,816, so this integer is abundant. The Collatz stopping time is 204 steps.

Prime Factor Structure

Factorization String 2^5 × 5 × 13 × 3677

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 19,463,976

Proper Divisor Sum 11,815,816

Digit Sum / Digital Root 32 (Root: 5)

Adjacent Primes #7648097 ← → #7648163

Radix Representation

Decimal	7648160
Binary	11101001011001110100000 (23 bits)
Octal	0o35131640
Hexadecimal	0x74B3A0

Divisor Catalog (48)

1 2 4 5 8 10 13 16 20 26 32 40 52 65 80 104 130 160 208 260 416 520 1,040 2,080 3,677 7,354 14,708 18,385 29,416 36,770 47,801 58,832 73,540 95,602 117,664 147,080 191,204 239,005 294,160 382,408 478,010 588,320 764,816 956,020 1,529,632 1,912,040 3,824,080 7,648,160

Collatz Trajectory (204 steps to reach 1)

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

7,648,160 3,824,080 1,912,040 956,020 478,010 239,005 717,016 358,508 179,254 89,627 268,882 134,441 403,324 201,662 100,831 302,494 151,247 453,742 226,871 680,614 340,307 1,020,922 510,461 1,531,384 765,692 382,846 191,423 574,270 287,135 861,406 430,703 1,292,110 646,055 1,938,166 969,083 2,907,250 1,453,625 4,360,876 2,180,438 1,090,219 3,270,658 1,635,329 4,905,988 2,452,994 1,226,497 3,679,492 1,839,746 919,873 2,759,620 1,379,810 689,905 2,069,716 1,034,858 517,429 1,552,288 776,144 388,072 194,036 97,018 48,509

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