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RE: Daily quiz #011 - what number should replace the question mark

in #mathematics6 years ago

An alternate answer: the product of every number in the triangle has nine prime factors.

8 * 44 * 3 = 2^5 * 3 * 11, which is 7 prime factors. The least number that can be multiplied to give 9 prime factors is 4.

7 * 32 * 9 = 2^5 * 3^2 * 7 , which which is 8 prime factors. The least numbers that can be multiplied to give 9 prime factors is 2.

7 * 75 * 8 = 2^3 * 3 * 5^2 * 7, which is 7 prime factors, again. So we should multiply by 4 to get two additional prime factors.

Therefore, the question mark should obviously be 4.

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