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Find the greatest common factor of 10,30 , and 45 .

Find the greatest common factor of $10$ , $30$ , and $45$ .

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Greatest common factor of three or four numbers

Full solution

Q. Find the greatest common factor of

10

,

30

, and

45

.

Factors of $10$ : List the factors of $10$ . $\newline$ To find the factors of $10$ , we look for numbers that divide $10$ without leaving a remainder. $\newline$ $1 \times 10 = 10$ $\newline$ $2 \times 5 = 10$ $\newline$ Factors of $10$ : $1, 2, 5, 10$
Factors of $30$ : List the factors of $30$ . $\newline$ To find the factors of $30$ , we look for numbers that divide $30$ 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 $45$ : List the factors of $45$ . $\newline$ To find the factors of $45$ , we look for numbers that divide $45$ without leaving a remainder. $\newline$ $1 \times 45 = 45$ $\newline$ $3 \times 15 = 45$ $\newline$ $5 \times 9 = 45$ $\newline$ Factors of $45$ : $1$ , $3$ , $5$ , $45$ $0$ , $45$ $1$ , $45$
Common Factors of $10$ , $30$ , and $45$ : Identify the common factors of $10$ , $30$ , and $45$ . $\newline$ We look for factors that are present in all three lists. $\newline$ Factors of $10$ : $1$ , $2$ , $5$ , $10$ $\newline$ Factors of $30$ : $1$ , $2$ , $30$ $1$ , $5$ , $30$ $3$ , $10$ , $30$ $5$ , $30$ $\newline$ Factors of $45$ : $1$ , $30$ $1$ , $5$ , $45$ $1$ , $30$ $5$ , $45$ $\newline$ The common factors are $1$ and $5$ .
Greatest Common Factor (GCF) of $10$ , $30$ , and $45$ : Find the Greatest Common Factor (GCF) of $10$ , $30$ , and $45$ . $\newline$ The common factors of $10$ , $30$ , and $45$ are $1$ and $30$ $0$ . Among these, $30$ $0$ is the greatest. $\newline$ GCF of $10$ , $30$ , and $45$ : $30$ $0$

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