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Find the greatest common factor of 18,36 , and 45 .

Find the greatest common factor of $18$ , $36$ , and $45$ .

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Greatest common factor of three or four numbers

Full solution

Q. Find the greatest common factor of

18

,

36

, and

45

.

Factors of $18$ : List the factors of $18$ . $\newline$ To find the factors of $18$ , we look for pairs of numbers that multiply to give $18$ . $\newline$ $1 \times 18 = 18$ $\newline$ $2 \times 9 = 18$ $\newline$ $3 \times 6 = 18$ $\newline$ Factors of $18$ : $1, 2, 3, 6, 9, 18$
Factors of $36$ : List the factors of $36$ . $\newline$ To find the factors of $36$ , we look for pairs of numbers that multiply to give $36$ . $\newline$ $1 \times 36 = 36$ $\newline$ $2 \times 18 = 36$ $\newline$ $3 \times 12 = 36$ $\newline$ $4 \times 9 = 36$ $\newline$ $6 \times 6 = 36$ $\newline$ Factors of $36$ : $1, 2, 3, 4, 6, 9, 12, 18, 36$
Factors of $45$ : List the factors of $45$ . $\newline$ To find the factors of $45$ , we look for pairs of numbers that multiply to give $45$ . $\newline$ $1 \times 45 = 45$ $\newline$ $3 \times 15 = 45$ $\newline$ $5 \times 9 = 45$ $\newline$ Factors of $45$ : $1$ , $3$ , $5$ , $9$ , $15$ , $45$
Common factors of $18$ , $36$ , and $45$ : Identify the common factors of $18$ , $36$ , and $45$ . $\newline$ We look for factors that are common to all three numbers. $\newline$ Common factors of $18$ , $36$ , and $45$ : $1$ , $36$ $0$ , $36$ $1$
Greatest Common Factor (GCF) of $18$ , $36$ , and $45$ : Find the Greatest Common Factor (GCF) of $18$ , $36$ , and $45$ . $\newline$ The common factors are $1$ , $3$ , and $9$ . The greatest of these is $9$ . $\newline$ GCF of $18$ , $36$ , and $45$ : $9$

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