46,972,872

2³ × 3⁵ × 73 × 331

46,972,872 factors as 2^3 × 3^5 × 73 × 331. Its 96 positive divisors give a proper-divisor sum of 87,168,408, so this integer is abundant. The Collatz stopping time is 178 steps.

Prime Factor Structure

Factorization String 2^3 × 3^5 × 73 × 331

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 134,141,280

Proper Divisor Sum 87,168,408

Digit Sum / Digital Root 45 (Root: 9)

Adjacent Primes #46972811 ← → #46972873

Radix Representation

Decimal	46972872
Binary	10110011001011111111001000 (26 bits)
Octal	0o263137710
Hexadecimal	0x2CCBFC8

Divisor Catalog (60 of 96)

1 2 3 4 6 8 9 12 18 24 27 36 54 72 73 81 108 146 162 216 219 243 292 324 331 438 486 584 648 657 662 876 972 993 1,314 1,324 1,752 1,944 1,971 1,986 2,628 2,648 2,979 3,942 3,972 5,256 5,913 5,958 7,884 7,944 8,937 11,826 11,916 15,768 17,739 17,874 23,652 23,832 24,163 26,811

Collatz Trajectory (178 steps to reach 1)

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

46,972,872 23,486,436 11,743,218 5,871,609 17,614,828 8,807,414 4,403,707 13,211,122 6,605,561 19,816,684 9,908,342 4,954,171 14,862,514 7,431,257 22,293,772 11,146,886 5,573,443 16,720,330 8,360,165 25,080,496 12,540,248 6,270,124 3,135,062 1,567,531 4,702,594 2,351,297 7,053,892 3,526,946 1,763,473 5,290,420 2,645,210 1,322,605 3,967,816 1,983,908 991,954 495,977 1,487,932 743,966 371,983 1,115,950 557,975 1,673,926 836,963 2,510,890 1,255,445 3,766,336 1,883,168 941,584 470,792 235,396 117,698 58,849 176,548 88,274 44,137 132,412 66,206 33,103 99,310 49,655

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