The factors of 34 are:
1, 2, 17, 34
The factors of 51 are:
1, 3, 17, 51
The common factors are:
1, 17
The Greatest Common Factor:
GCF = 17
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Prime factorisation.
34 = 2*17
51 = 3*17
The only prime factor that is common to both is 17.
So GCF(34, 51) = 17