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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.

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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Q: What are a pair of numbers that are relatively prime?

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