1,2,5 and 10 are factors of ten.
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Increasing by a factor of ten is to multiply by 10. By extension, decreasing by a factor of 2 would be to divide by 2.
The two numbers that have the greatest common factor of ten are any two multiples of ten. This is because the greatest common factor is the largest number that divides evenly into both numbers. So, for example, 10 and 20 have a greatest common factor of 10 because 10 is the largest number that divides evenly into both 10 and 20.
Six and ten's highest common factor is two.
The GCF is 10.
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