Yes.
The factors of 100 are 2,2,5 and 5 i.e. 100 = 10 x 10 and 10 = 2 x 5 so 100 = 2 x 2 x 5 x 5
81 is the square of 9 (i.e. 81 = 9 x 9)
9 is also the square of 3 (i.e. 9 = 3 x 3 )
So the factors of 81 are 9 x 9 = 3 x 3 x 3 x 3
Now it is clear that the two original numbers have no common factors and therefore they are "relatively prime" though neither alone is a Prime number as they are both squares.
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The factors of 37 are 1 and 37. The factors of 81 are 1, 3, 9, 27, and 81. They have only one factor in common - 1. Since the greatest common factor of 37 and 81 is 1, they are relatively prime. You can also look at the prime factors to determine the greatest common factor. 37 is a prime number, so its only prime factor is itself, 37. The prime factors of 81 are 3, 3, 3, and 3. They have no prime factors in common, so they are relatively prime, which means their greatest common factor is 1.
The LCM is 5184. The numbers 81 and 64 have no common factors. When you have two relatively prime numbers, you find their LCM by multiplying them. So 5184 is 81x64.
22 is not relatively prime
yes, they are relatively prime.
81 = 3^4 so 3 is a prime factor.