Question

1. (1) the factors of 12 are 1, 2, 3, 4, □, 12. (2) the factors of 18 are 1, 2, 3, □, 9, 18. (3) the factors of both 12 and 18 are 1, 2, □, □. these are called the common factors of 12 and 18. (4) among the common factors, the largest one is called the greatest common factor (gcf). the gcf of 12 and 18 is □. 4. divide the numerator and the denominator by the gcf of 12 and 18. \\(\frac{12}{18}=\frac{□}{□}\\) fractions can be reduced in one step by using the gcf.

Explanation:

Step1: List factors of 12

Find all numbers dividing 12: $1, 2, 3, 4, 6, 12$

Step2: List factors of 18

Find all numbers dividing 18: $1, 2, 3, 6, 9, 18$

Step3: Find common factors

Identify shared factors of 12 & 18: $1, 2, 3, 6$

Step4: Find GCF of 12 & 18

Select largest common factor: $6$

Step5: Simplify $\frac{12}{18}$

Divide numerator/denominator by GCF 6: $\frac{12\div6}{18\div6}=\frac{2}{3}$

Answer:

1. (1) $\boldsymbol{6}$

(2) $\boldsymbol{6}$
(3) $\boldsymbol{3}$, $\boldsymbol{6}$
(4) $\boldsymbol{6}$

1. $\boldsymbol{\frac{2}{3}}$