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Yes, 45 and 64 are relatively prime because they do not share any prime factors.
9 prime factors --> 3,3 15 prime factors --> 5,3 45 prime factors --> 5,3,3 They all share 3 therefore: "3"; Between 9 and 45 they share: 3,3 ----for 9 & 45 gcf is 3*3 = 9;
18 and 81 share only one prime factor: 3
In prime factors (divisors) 187 = 11x17 and 1000 = 2x2x2x5x5x5 So they share no prime factors and this is referred to as being co-prime or relatively prime. In this case the highest common factor (or greatest common divisor) is 1.
Two numbers which are "relatively prime" have no common prime factors. To illustrate, let's write several numbers in terms of their prime factors: 24 = 2 x 2 x 2 x 3 25 = 5 x 5 42 = 2 x 3 x 7 70 = 2 x 5 x 7 You can see that 24 and 25 are relatively prime, because they don't share any common prime factors. Likewise, 25 and 42 are relatively prime. 24 and 42, however, are NOT relatively prime because they share the common factors of 2 and 3. Likewise 25 and 70 are NOT relatively prime because they share the common factor 5. When a fraction is in its simplest form, the numerator and denominator are relatively prime.