Question

How do you find the GCF of 80 and 25?

Answer 1

Hint: We know that GCF stands for the highest common factor. To find the GCF of two given numbers, we first need to find the prime factors of each one. After that we will find the common factors in both. The largest number that can be obtained by multiplying the common factors will be the GCF of the two given numbers.

Complete step by step answer:
We will first find the prime factors of 80.
As the unit digit of 80 is 0, it can be divided by 2and hence we can write it as:
\[80 = 40 \times 2\]
Now. The unit digit of 40 is also 0, therefore it can also be divided by 2.
\[ \Rightarrow 80 = 20 \times 2 \times 2\]
We can see that similarly 20 can also be divided by 2.
\[ \Rightarrow 80 = 10 \times 2 \times 2 \times 2\]
Furthermore, 10 can also be divided by 2.
\[ \Rightarrow 80 = 5 \times 2 \times 2 \times 2 \times 2\]
Here, we can observe that all the factors are prime numbers.
Now, we will do the same procedure for the second number which is 25.
As we can see that the unit digit of 25 is 5, it can be divided by 5 and hence it can be written as:
\[25 = 5 \times 5\]
We have obtained the prime factors of 25 in this first step only.
Thus, we have now two numbers with their prime factors.
\[80 = 5 \times 2 \times 2 \times 2 \times 2\]
\[25 = 5 \times 5\]
We can see that there is only one common factor in both numbers which is 5.
Hence, we can say that the GCF of 80 and 25 is 5.

Note: The GCF is also known as the Highest Common Factor or HCF. We need to keep in mind that if the two numbers given are prime numbers, then they will not have any factors in common. In this case, their GCF will be 1.