All even numbers have 2 as a factor, but no odd numbers do. The only even number that will appear as a factor in prime factorizations is 2, because it is the only even Prime number. Thus, an odd number will not have even numbers in its prime factorization because an odd number is not evenly divisible by 2.
The only even numbers that could appear in the exponential form are the exponents. For example 81 is 34. The factor is an odd number - 3, while the exponent is an even number - 4.
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No, it is never bigger than the smaller number.
When one of the numbers is a factor of the other.
Real numbers are composed of rational and irrational numbers. Integers are part of the group (set) of rational numbers. And the integers are composed of the counting numbers (1, 2, 3, ...) and their negative counterparts (-1, -2, -3, ...). Oh, almost forgot. There is one more integer that is neither positive or negative. It's the number zero. Zero is an integer (neither positive or negative). The smallest real number ever is zero.
I can't give you an example of when that happens because that doesn't ever happen. The GCF of a pair of numbers can't be larger than the smaller number.
No, it's never greater than the smallest number.