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Hey, this is Presh Talwalkar reminding you to mind your decisions.

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Congratulations to Daniel Mai, 13 years old, for winning the 2019 Raytheon Math Counts

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National Competition.

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The prize includes a $20,000 college scholarship.

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The final round was a speed test competition between Mai and Suyash Pandit.

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It was pencil and paper only, no calculators were allowed.

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Here's the question that sealed the victory.

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What is the quotient of 5040 divided by the product of its unique prime factors?

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Pause the video right now if you'd like to give it a try, and when you're ready, keep

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watching the video for a solution.

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To solve this problem, we need to find the prime factorization of 5040.

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Since it's an even number, it's divisible by 2.

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Since 2520 is an even number, we can divide by 2 again.

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And then 1260 is an even number, so we divide by 2 again.

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630 is also even, so we divide by 2 again.

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315 is odd, so we can't divide by 2 any more times. Now the digits of

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315 are 3, 1, and 5. If we add them together we get 9. So 315 will be divisible by 9.

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So it will be divisible by 3, and it'll be divisible by 3 again.

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Now 35 is equal to 5 times 7. This is the prime factorization of 5040.

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We need the quotient of this with it's unique prime factors.

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The unique prime factors are 2, 3, 5, and 7.

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We divide both sides by 2, 3, 5, and 7, and we end up with the quotient of 5040 by it's unique prime factors.

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The result will be 2 cubed times 3, and that's equal to 24.

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And that's our answer.

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It took me a couple of minutes to do this calculation and to be sure that I got the correct answer.

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but Mai solved this question in only seconds.

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Congratulations again!

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And who knows, with all the smart viewers on Mind Your Decisions,

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maybe the winner of next year's Math Counts competition

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is watching this video right now.

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Thanks for watching and for making Mind Your Decisions

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one of the best channels on YouTube.

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Thanks for watching and thanks for your support.