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Hello everyone, welcome to pay attention to the Olympic mathematics easy to learn, I am the Olympic mathematics Teacher Yu, in this waiting for you for a long time, today to bring you 3 interesting questions, belongs to the cup competition common exam question type.

Waste

Without further ado, I'll start with the question:

The sum of two non-zero natural numbers is 210 and the least common multiple is 1547, so what is their product?

The topic belongs to the problem of number theory. The solution idea can be reduced to the following three problems:

Topic 1 (Simple)

Find the greatest common divisor of 210 and 1547.

Topic 2 (Medium Difficulty)

The sum of the two non-zero natural numbers is 210, and the least common multiple is 1547, which is the greatest common divisor of these two natural numbers.

Topic 3 (Advanced Thinking, Real Questions of the Chinese Cup)

Just wait for you, welcome to start your smart brain, write the answer in the article comment area! In the next issue, I will publish the answer to today's question!

Previous Answers:

Topic 1:

A: 2, 3, 5, 7, 11, 13, 17, 19.

Topic 2:

A: No.

Because the three prime numbers of 13, 17, and 19, in 1-22, are not factors of any number.

Regardless of the combination, at least one number with 1 of the above 3 numbers as the numerator or denominator is the fraction.

Topic 3:

A: 10.

To make as many integers as possible, first the primes are sorted, and then the remaining, such as:

19/17，13/1，22/11，14/7，15/5，21/3，20/10，18/9，16/8，12/6，4/2。

There are a total of 10 integers in the above arrangement,

As you know from title two, there can be no 11 integers.

So, the answer is 10.

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