Chapter 5: divisibility and the greatest common factor (1)


Suppose m and N are integers,m\neq 0。 If n is a multiple of M, there exists an integer k such thatn= mk。 If M is divisible by N, we write it asm|n; ifmDo not dividen, we remember asm\nmid n。 For example, because6=3·2, so3|66The factor of is1,2,3。 Because there is no5A multiple of is equal to7, so5\nmid7。 to be divisible bynIs callednFactor.

If we know two integers, we can find their common factor, that is, divide them by their two numbers. For example, because4|12And4|20, so4yes12And20The common factor of. be careful,4yes12And20The greatest common factor of. Similarly,3yes18And30The common factor of, but not the largest, because6It is also a common factor.

Two numbersaAndbThe greatest common factor of (not all zero) is the largest number divisible by both of themgcd(a,b)。 Ifgcd(a,b)=1We call itaAndbMutual prime.

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