Question

# Find the common factors of $56$ and $120$.

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Hint: Try to find individual factors.

A factor of a number is another number that divides it without leaving a remainder.
Given the two numbers $56$ and $120$.
First, we need to find the factors of each number individually.
Factors of $56$ are: ${S_1} = \left\{ {1,2,4,7,8,14,28,56} \right\}$
Factors of $120$are: ${S_2} = \left\{ {1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120} \right\}$
The common numbers in set ${S_1}$ and ${S_2}$are,
${S_1} \cap {S_2} = \left\{ {1,2,4,8} \right\}$
Hence the common factors of $56$ and $120$are $\left\{ {1,2,4,8} \right\}$ .

Note: The highest common factor is always less than equal to the lowest number involved.
Prime numbers have only one common factor that is $1$ .