7,638,225

3 × 5² × 7 × 14549

7,638,225 has the prime decomposition 3 × 5^2 × 7 × 14549. Its 4 distinct prime factors produce 24 positive divisors.

Prime Factor Structure

Factorization String 3 × 5^2 × 7 × 14549

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 14,433,600

Proper Divisor Sum 6,795,375

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #7638173 ← → #7638227

Radix Representation

Decimal	7638225
Binary	11101001000110011010001 (23 bits)
Octal	0o35106321
Hexadecimal	0x748CD1

Divisor Catalog (24)

1 3 5 7 15 21 25 35 75 105 175 525 14,549 43,647 72,745 101,843 218,235 305,529 363,725 509,215 1,091,175 1,527,645 2,546,075 7,638,225

Collatz Trajectory (217 steps to reach 1)

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

7,638,225 22,914,676 11,457,338 5,728,669 17,186,008 8,593,004 4,296,502 2,148,251 6,444,754 3,222,377 9,667,132 4,833,566 2,416,783 7,250,350 3,625,175 10,875,526 5,437,763 16,313,290 8,156,645 24,469,936 12,234,968 6,117,484 3,058,742 1,529,371 4,588,114 2,294,057 6,882,172 3,441,086 1,720,543 5,161,630 2,580,815 7,742,446 3,871,223 11,613,670 5,806,835 17,420,506 8,710,253 26,130,760 13,065,380 6,532,690 3,266,345 9,799,036 4,899,518 2,449,759 7,349,278 3,674,639 11,023,918 5,511,959 16,535,878 8,267,939 24,803,818 12,401,909 37,205,728 18,602,864 9,301,432 4,650,716 2,325,358 1,162,679 3,488,038 1,744,019

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