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# NUMBER THEORY

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What is the greatest common factor of 20! and 200,000? I got 20,000, but that is incorrect. Explain your method.

Nov 17, 2019

#1
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Prime factorize 200,000

\(2^6*5^5\)

20! is pretty much already factored for you.

For visualization, we have 20 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8  * 7 * 6 * 5 * 4 * 3 * 2 * 1

Since we have this, \(2^6*5^5\), we try to find the maximum number of 2s and 5s from 20! that can fit into the prime factorization.

We easily have six 2s, and we only have four 5s.

So we evaluate \(2^6 * 5^4\), and get the answer.

I will leave that up to you.

Nov 17, 2019

#1
+2

Prime factorize 200,000

\(2^6*5^5\)

20! is pretty much already factored for you.

For visualization, we have 20 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8  * 7 * 6 * 5 * 4 * 3 * 2 * 1

Since we have this, \(2^6*5^5\), we try to find the maximum number of 2s and 5s from 20! that can fit into the prime factorization.

We easily have six 2s, and we only have four 5s.

So we evaluate \(2^6 * 5^4\), and get the answer.

I will leave that up to you.

CalculatorUser Nov 17, 2019
#2
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Nice, CU !!!!   CPhill  Nov 17, 2019