Q: What is a number where the first factor is greater than or equal to one and less than ten and the second factor is a power of ten?

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What is the question for this situation

equal to or greater than

Assuming the second even number is equal to 4 or greater, than the highest common factor of the two numbers is equal to an even number 2 or greater. Why can't an odd factor be used? Any odd factor must be multiplied by (at least) 2 to create an even product (ie. the 1st even number). That same odd factor must be multiplied by (at least 2) and any other number to create a 2nd even product, thereby making the Greatest Common Factor (at least) 2 times the odd number....which is an even number.

No. All factors of a number are less than or equal to it. Therefore the highest factor of 12 is 12. The common factor of 12 with any other number (greater than) 12 cannot be greater than the highest factor of 12 which is 12. Thus no. [The hcf(12, 30) = 6.]

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What is the question for this situation

equal to or greater than

Assuming the second even number is equal to 4 or greater, than the highest common factor of the two numbers is equal to an even number 2 or greater. Why can't an odd factor be used? Any odd factor must be multiplied by (at least) 2 to create an even product (ie. the 1st even number). That same odd factor must be multiplied by (at least 2) and any other number to create a 2nd even product, thereby making the Greatest Common Factor (at least) 2 times the odd number....which is an even number.

Greater. It cannot be equal because there is not even a 7 in the second number!

When they have a factor in common greater than one.

No. At most, it can be equal to the smaller number.

No. All factors of a number are less than or equal to it. Therefore the highest factor of 12 is 12. The common factor of 12 with any other number (greater than) 12 cannot be greater than the highest factor of 12 which is 12. Thus no. [The hcf(12, 30) = 6.]

As a general rule, multiples tend to be larger than factors. This is not always true. 9 is a factor of 27. 6 is a multiple of 3. The important distinction is in the relationship to the number they are factors or multiples of. A factor will be equal to or lesser than the number. A multiple will be equal to or greater than the number.

They are both equal. There is simply an extra zero added on the end of the second number.

No there is not. If you are looking for prime factors of a number and you get to the square root of that number you can stop. Yes, there is. If an integer is not itself a prime, then one of its factors will be less or equal to its square root and the "co-factor" will be greater than or equal to the square root. But both cannot be greater than the square root so, when searching for factors, you can stop when you reach the square root.

A number cannot be greater than and equal to another number at the same time.

A number times a number is a factor times a factor and it makes a product. Number x number = factor x factor = product