7,948,225

5² × 23² × 601

Starting at 7,948,225, the Collatz iteration reaches 1 after 217 steps. The first transition is 23844676; the starting value is odd with 18 positive divisors.

Prime Factor Structure

Factorization String 5^2 × 23^2 × 601

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 18

Divisor Sum (σ) 10,320,086

Proper Divisor Sum 2,371,861

Digit Sum / Digital Root 37 (Root: 1)

Adjacent Primes #7948223 ← → #7948247

Radix Representation

Decimal	7948225
Binary	11110010100011111000001 (23 bits)
Octal	0o36243701
Hexadecimal	0x7947C1

Divisor Catalog (18)

1 5 23 25 115 529 575 601 2,645 3,005 13,225 13,823 15,025 69,115 317,929 345,575 1,589,645 7,948,225

Collatz Trajectory (217 steps to reach 1)

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

7,948,225 23,844,676 11,922,338 5,961,169 17,883,508 8,941,754 4,470,877 13,412,632 6,706,316 3,353,158 1,676,579 5,029,738 2,514,869 7,544,608 3,772,304 1,886,152 943,076 471,538 235,769 707,308 353,654 176,827 530,482 265,241 795,724 397,862 198,931 596,794 298,397 895,192 447,596 223,798 111,899 335,698 167,849 503,548 251,774 125,887 377,662 188,831 566,494 283,247 849,742 424,871 1,274,614 637,307 1,911,922 955,961 2,867,884 1,433,942 716,971 2,150,914 1,075,457 3,226,372 1,613,186 806,593 2,419,780 1,209,890 604,945 1,814,836

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