The derivation of "factor" is from Latin, through French and Middle English.
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The word is from Latin - per centum meaning by the hundred
A factor is a number or quantity that when multiplied with another produces a given number or expression.
For every factor of a number, there is another factor that results when you divide the first factor into the number. Factors can be listed in pairs. Since 9 x 4 = 36, (9,4) is a factor pair of 36.
The greatest common factor of 27 and 30 is 3
The greatest common factor of 10 and 70 is 10.