A and B said at the same time: I know.
So what are these three digits?
analyse
Let's review the knowledge about divisor first.
A prime number has only two divisors, one is 1 and the other is itself; So the divisor of a prime number is always 2.
A composite number can be expressed as the product of its prime factors, for example
If a composite number has only one prime factor and can be expressed as, then its divisor is;
If a composite number has only two prime factors and can be expressed as, then its divisor is;
More prime factors, and so on.
In other words, the divisor of the composite number can be obtained by adding 1 to the exponents of all prime factors and then multiplying them.
Now back to this topic. Because the number of factors is prime, there is only one prime.
Because it is a composite number, the exponent of the prime factor is greater than1;
So we know it should be a number similar to this.
There is another requirement in the known condition: it is three digits, which means it should be between and.
Not many people meet the above requirements, and a list can be compiled immediately.
As can be seen from the above list, these two numbers are "very personal" and appear only once, but twice. Other figures (including) appear many times and lack individuality.
If only one student knows the value; Now there are two students who answer the value they know at the same time, which means:
Refine and improve
Divisor is a basic knowledge point of elementary number theory, and it is also a common test point in primary school mathematics competition.
This topic combines number theory and logical reasoning, which is not difficult and more fun.