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Q: Is the greatest common factor of a pair of numbers ever greater than both numbers explain with an example?

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The Greatest Common Factor depends upon the numbers for which there are common factors and it is the greatest one of them; it can be greater than 18, for example the greatest common factor of 40 and 100 is 20. The greatest common factor must be one of the factors of each of the numbers. As the factors of each number cannot be greater than that number, the greatest common factor of a set of numbers cannot be greater than the least number. If this number is not greater than 18 then the greatest common factor of the numbers cannot be greater than 18. Even if the least number is greater than 18 it is possible that the greatest common factor of a set of numbers is still not greater than 18, for example the greatest common factor of 20, 30 and 50 is 10.

No, square numbers greater than 1 have more than two factors.

Sure there are greater numbers. For example, 4 is greater than 3. If you mean "... no greatest number", the reason is that you can always add one more, and get a number that is even greater. Thus, for example, 10 is not the greatest number, because you can add one and get 11. 11 is not the greatest number either, because you can add one and get 12. Etc.

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.

There are infinitely many numbers: for example any number greater than 6, for example.

§ In comparing two whole numbers, the one with the most digits is always the greater number. § In decimals the number with the greatest number of digits is not always the greatest.

No.

Yes it is.

No, the greatest common factor is never greater than the smallest number. The greatest common factor is the largest integer that divides evenly into all of the numbers listed.

No, the GCF is the lesser of the numbers.

12

No.

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