No, it's never greater than the lesser number.
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No, a factor of something is a piece of it, and a piece of something cannot be greater than the whole thing.
A number can't have a factor greater than itself, so the GCF of a pair of numbers can't ever be greater than the smaller number. The GCF of 9 and 18 is 9.
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A prime number is an integer which is greater than one and which is evenly divisible only by one and itself. A pair of prime numbers consists of two such numbers.
The LCM is never less than the greatest number in the set. The LCM of 4 and 9 is 36.
The sum of any pair of prime numbers greater than 2 is an even number.