420,072

2³ × 3 × 23 × 761

420,072 is even and not a perfect square. Its factorization is 2^3 × 3 × 23 × 761 and its 32 divisors sum to 1,097,280.

Prime Factor Structure

Factorization String 2^3 × 3 × 23 × 761

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 1,097,280

Proper Divisor Sum 677,208

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #420047 ← → #420073

Radix Representation

Decimal	420072
Binary	1100110100011101000 (19 bits)
Octal	0o1464350
Hexadecimal	0x668E8

Divisor Catalog (32)

1 2 3 4 6 8 12 23 24 46 69 92 138 184 276 552 761 1,522 2,283 3,044 4,566 6,088 9,132 17,503 18,264 35,006 52,509 70,012 105,018 140,024 210,036 420,072

Collatz Trajectory (55 steps to reach 1)

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

420,072 210,036 105,018 52,509 157,528 78,764 39,382 19,691 59,074 29,537 88,612 44,306 22,153 66,460 33,230 16,615 49,846 24,923 74,770 37,385 112,156 56,078 28,039 84,118 42,059 126,178 63,089 189,268 94,634 47,317 141,952 70,976 35,488 17,744 8,872 4,436 2,218 1,109 3,328 1,664 832 416 208 104 52 26 13 40 20 10 5 16 8 4 2 1

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