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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.
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What pair of numbers is relatively prime 10 and 21 12 and 54 15 and 27 21 and 39?
I suggest factoring each pair of numbers, and checking whether they have, or don't have, common factors. A pair of numbers is said to be "relatively prime" if they have no common factors (their greatest common factor is 1). For larger numbers, Euclid's algorithm could be used, but for such small numbers, factoring is probably faster.
True or false if two numbers a relatively prime one of the must be prime?
False. Consider 4 and 9. Neither are prime, but they have no common factors other than 1 and are therefore relatively prime. More generally, any two numbers p^n and q^n where p, q both prime and n<>p or q and n>1 are relatively prime. This is by no means all pairs of relatively prime numbers, but it's an easy way to find examples where neither of the pair is prime.
What two numbers have 1 as there gcf?
Prime and relatively prime numbers all have a GCF of 1.
Is 12 and 35 relatively prime?
12 and 35 are NOT prime numbers.
Is 45 and 64 relatively prime?
Numbers are either prime or they aren't. In this case, 45 is divisible by 3 and 15; sixty-four goes into 2, 4, 8 and 32. The term "relatively prime" compares two numbers and their common factors. If the GCF of the two numbers is 1, then they are "relatively prime."
