Relative Primes
“Master, what are relative primes,” asked Lanoo.
“Lanoo, they are two integers that cannot be divided by any one prime number. The only common divisor of the two numbers is 1,” replied the Master.
“Does that mean that if I have two different integers, no prime number will divide both of them,” repeated Lanoo.
“Yes, indeed,” smiled the Master. “You might try working out the probability that any two random integers less than 100 will be relatively prime,” challenged the Master.
“I will certainly give it a try,” said Lanoo eagerly, pulling out a notebook and a pencil.
Can you help Lanoo work this out? Could the probability you obtain also apply in some way to any two integers greater than 100 picked at random?
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