What is the GCF of 25 and 40?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 25 and 40. To solve it, we will identify the factors of both numbers and determine the largest factor they share.
Answer
The greatest common factor of 25 and 40 is $5$.
Answer for screen readers
The greatest common factor (GCF) of 25 and 40 is $5$.
Steps to Solve
- Identify the factors of 25
To find the factors of 25, we look for numbers that divide 25 without leaving a remainder. The factors are: $$ 1, 5, 25 $$
- Identify the factors of 40
Next, we find the factors of 40, which are: $$ 1, 2, 4, 5, 8, 10, 20, 40 $$
- Find the common factors
Now, we list the common factors between 25 and 40. From the two sets of factors, we see that: $$ 1, 5 $$ are the common factors.
- Determine the greatest common factor
Finally, among the common factors, the greatest one is $5$.
The greatest common factor (GCF) of 25 and 40 is $5$.
More Information
The GCF is useful in various mathematical applications, such as simplifying fractions and solving problems related to ratios. Understanding the GCF can also help when working with polynomial expressions in algebra.
Tips
- One common mistake is to confuse the GCF with the least common multiple (LCM). Make sure to identify whether the problem is asking for GCF or LCM.
- Not listing all factors completely can lead to missing the GCF. Always ensure to carefully list all factors of each number.
