Question

How do you find the greatest common factor of 55, 75?

Answer 1

Hint: To find the greatest common factor of two numbers, we need to follow some steps, the steps are as follows
Step 1: Find all factors of the number.
Step 2: Make a list of their common factors.
Step 3: The largest number in the list is their greatest common factor.

Complete step-by-step solution:
The given two numbers are \[55\], and \[75\]. We have to find the greatest common factor. To find the greatest common factor of any two numbers, we have to follow some steps. We will follow these steps for these numbers.
The first step is to find all factors of the given numbers. The factors of \[55\] are \[1,\text{ }5,\text{ }11,\] and the number itself is \[55\]. The factors of \[75\] are \[1,\text{ }3,\text{ }5,\text{ }15,\text{ }25,\] and the number itself is \[75\].
The next step is to make a list of their common factors. Here the common factors of \[55\], and \[75\] is \[5\] only.
In the last step, we make a list of the common factors. As both have only one factor common, this factor is their greatest common factor.
Hence, the greatest common factor (GSF) of \[55\], and \[75\] is \[5\].

Note: Here both numbers have only one common factor, so this is their GCF. If the numbers have more than one common factor, we have to find the largest of them.
In some cases, it becomes difficult to find the GCF due to a large number of factors of a number, etc. For such cases, we first find the Lowest common multiple (LCM) of the numbers, and then calculate their GCF by using the following property, which states that for any two given numbers the product of their LCM and GCF is equal to the product of the given numbers.
\[\Rightarrow LCM\times GCF=a\times b\]
Here \[a\And b\] are the given numbers.