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Find the greatest common factor of 30 and 18.

Find the greatest common factor of $30$ and $18$ .

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Greatest common factor

Full solution

Q. Find the greatest common factor of

30

and

18

.

Factors of $30$ : List the factors of $30$ . $\newline$ To find the factors of $30$ , we list all the numbers that $30$ can be divided by without leaving a remainder. $\newline$ $1 \times 30 = 30$ $\newline$ $2 \times 15 = 30$ $\newline$ $3 \times 10 = 30$ $\newline$ $5 \times 6 = 30$ $\newline$ Factors of $30$ : $1, 2, 3, 5, 6, 10, 15, 30$
Factors of $18$ : List the factors of $18$ . $\newline$ Similarly, we list all the numbers that $18$ can be divided by without leaving a remainder. $\newline$ $1 \times 18 = 18$ $\newline$ $2 \times 9 = 18$ $\newline$ $3 \times 6 = 18$ $\newline$ Factors of $18$ : $1, 2, 3, 6, 9, 18$
Common factors of $30$ and $18$ : Identify the common factors of $30$ and $18$ . $\newline$ We look for numbers that are factors of both $30$ and $18$ . $\newline$ Common factors of $30$ and $18$ : $1$ , $2$ , $3$ , $6$
Greatest Common Factor of $30$ and $18$ : Find the Greatest Common Factor (GCF) of $30$ and $18$ . $\newline$ The common factors are $1$ , $2$ , $3$ , and $6$ . The greatest of these is $6$ . $\newline$ GCF of $30$ and $18$ : $6$

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