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How many positive divisors does 20 have?
Which of these numbers has the most divisors?
nPrime Factorization# of Divisors2022×5163021×31×5185021×5266022×31×51129021×32×511215021×31×521221021×31×51×71? \begin{array} {c|c|c} n & \text{Prime Factorization} & \text{\# of Divisors} \\ \hline 20 & 2^2 \times 5^1 & 6 \\ 30 & 2^1 \times 3^1 \times 5^1 & 8 \\ 50 & 2^1 \times 5^2 & 6 \\ 60 & 2^2 \times 3^1 \times 5^1 & 12 \\ 90 & 2^1 \times 3^2 \times 5^1 & 12 \\ 150 & 2^1 \times 3^1 \times 5^2 & 12 \\ 210 & 2^1 \times 3^1 \times 5^1 \times 7^1 & ? \end{array} n2030506090150210Prime Factorization22×5121×31×5121×5222×31×5121×32×5121×31×5221×31×51×71# of Divisors686121212? How many divisors does 210 have?
210=21×31×51×715=5115=31×5128=22×7135=51×7142=21×31×71 \begin{aligned} 210 &= 2^1 \times 3^1 \times 5^1 \times 7^1\\ \\ 5 &= 5^1\\ 15 &= 3^1 \times 5^1\\ 28 &= 2^2 \times 7^1\\ 35 &= 5^1 \times 7^1\\ 42 &= 2^1 \times 3^1 \times 7^1 \end{aligned} 210515283542=21×31×51×71=51=31×51=22×71=51×71=21×31×71 Which is not a divisor of 210?
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