Question

What is the greatest common factor of 75 and 30?

Answer 1

Hint: For solving this question you should know about the greatest common factor between two or more digits. For calculating the greatest common factor or GCF we will do factors of the given digits and then we will take all the common values. And see the greatest common value in this.

Complete step by step solution:
According to our question we have to calculate the greatest common factor of 75 and 30.
We can solve this by the factorization method. In this method we make factors of all digits which are given and then take the common digits outside and then we see the greatest common value in this.
If we see an example: 18, 27 find the GCF of these.
Then factors of 18: 1, 2, 3, 6, 9, 18
Factors of 27: 1, 3, 9, 27
The common factors of 18 and 27 are 1, 3 and 9. Among these numbers, 9 is the greatest (larger). Thus, the GCF of 18 and 27 is 9.
So, this can be written as: GCF (18, 27) = 9
OR we can solve this by this method also:
Step 1: Divide the larger no. by the smaller no. to give a quotient and remainder.
$$\Rightarrow {\displaystyle \frac{27}{18}}=1$$ with remainder 9
Step 2: If the remainder is zero then the smaller no. is GCF. But here it is not 0.
Step 3: Repeat with the smaller number and remainder this step again.
$$\Rightarrow {\displaystyle \frac{18}{9}}=2$$ with remainder 0.
Here, the remainder is zero. So, GCF (27, 18) = 9.
According to our question GCF for 75 and 30 is:
$$\Rightarrow {\displaystyle \frac{75}{30}}=2$$ with remainder 15
Now, repeat it again with smaller no. and remainder because remainder $$\ne 0$$.
So, $${\displaystyle \frac{30}{15}}=2$$ with remainder 0.
So, here the remainder is zero. The GCF (75, 30) = 15.

Note: During solving this question you can use any one method. But the first method is more tough and that has chances to be mistaken in the answer because the factors can be wrong and by mistake we can forget to take common from the factors any value. Then our answer will be wrong.