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Find the greatest common factor of 7,15 , and 21 .

Find the greatest common factor of $7$ , $15$ , and $21$ .

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Greatest common factor of three or four numbers

Full solution

Q. Find the greatest common factor of

7

,

15

, and

21

.

Factors of $7$ : List the factors of $7$ . $\newline$ $7$ is a prime number, so its only factors are $1$ and itself. $\newline$ Factors of $7$ : $1, 7$
Factors of $15$ : List the factors of $15$ . $\newline$ $1 \times 15 = 15$ $\newline$ $3 \times 5 = 15$ $\newline$ Factors of $15$ : $1$ , $3$ , $5$ , $15$
Factors of $21$ : List the factors of $21$ . $\newline$ $1 \times 21 = 21$ $\newline$ $3 \times 7 = 21$ $\newline$ Factors of $21$ : $1$ , $3$ , $7$ , $21$
Common factors of $7$ , $15$ , and $21$ : Identify the common factors of $7$ , $15$ , and $21$ . $\newline$ Factors of $7$ : $1$ , $7$ $\newline$ Factors of $15$ : $1$ , $15$ $1$ , $15$ $2$ , $15$ $\newline$ Factors of $21$ : $1$ , $15$ $1$ , $7$ , $21$ $\newline$ The only common factor is $1$ , since it is the only factor that appears in all three lists.
Greatest common factor (GCF) of $7$ , $15$ , and $21$ : Determine the greatest common factor (GCF) of $7$ , $15$ , and $21$ . $\newline$ Since the only common factor is $1$ , the GCF of $7$ , $15$ , and $21$ is $1$ .

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