67,772,536

2³ × 13 × 23 × 29 × 977

67,772,536 factors as 2^3 × 13 × 23 × 29 × 977. Its 64 positive divisors give a proper-divisor sum of 80,101,064, so this integer is abundant. The Collatz stopping time is 153 steps.

Prime Factor Structure

Factorization String 2^3 × 13 × 23 × 29 × 977

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 147,873,600

Proper Divisor Sum 80,101,064

Digit Sum / Digital Root 43 (Root: 7)

Adjacent Primes #67772503 ← → #67772569

Radix Representation

Decimal	67772536
Binary	100000010100010000001111000 (27 bits)
Octal	0o402420170
Hexadecimal	0x40A2078

Divisor Catalog (60 of 64)

1 2 4 8 13 23 26 29 46 52 58 92 104 116 184 232 299 377 598 667 754 977 1,196 1,334 1,508 1,954 2,392 2,668 3,016 3,908 5,336 7,816 8,671 12,701 17,342 22,471 25,402 28,333 34,684 44,942 50,804 56,666 69,368 89,884 101,608 113,332 179,768 226,664 292,123 368,329 584,246 651,659 736,658 1,168,492 1,303,318 1,473,316 2,336,984 2,606,636 2,946,632 5,213,272

Collatz Trajectory (153 steps to reach 1)

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

67,772,536 33,886,268 16,943,134 8,471,567 25,414,702 12,707,351 38,122,054 19,061,027 57,183,082 28,591,541 85,774,624 42,887,312 21,443,656 10,721,828 5,360,914 2,680,457 8,041,372 4,020,686 2,010,343 6,031,030 3,015,515 9,046,546 4,523,273 13,569,820 6,784,910 3,392,455 10,177,366 5,088,683 15,266,050 7,633,025 22,899,076 11,449,538 5,724,769 17,174,308 8,587,154 4,293,577 12,880,732 6,440,366 3,220,183 9,660,550 4,830,275 14,490,826 7,245,413 21,736,240 10,868,120 5,434,060 2,717,030 1,358,515 4,075,546 2,037,773 6,113,320 3,056,660 1,528,330 764,165 2,292,496 1,146,248 573,124 286,562 143,281 429,844

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