Question

What is the greatest common factor of $$30$$, $$45$$, and $$50$$?

Answer 1

Hint: Here in this question, we have to find the greatest common factor [GCF] of the given three numbers. To find this first we have to list out the factors of each number among the factors of three numbers, the largest common number which is the factor of all three numbers that number is known as the greatest common factor.

Complete step by step solution:
The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The GCF of two natural numbers x and y is the largest possible number which divides both x and y. "Greatest Common Factor" is also known as Highest Common Divisor (HCD) or Highest Common Factor (HCF) or Greatest Common Divisor (GCD).
There are 3 methods for finding the greatest common factor of two numbers.
Listing Out Common Factors
Prime Factorization
Division Method
In the question, the given we have to find the greatest common factor of $$30$$, $$45$$, and $$50$$
Now, find GCF by Listing Out the Common Factors
In this method, we have to list out the factors of all three numbers i.e., $$30$$, $$45$$, and $$50$$
Factors of $$30$$: $$\left\{1,2,3,5,6,10,15,30\right\}$$
Factors of $$45$$: $$\left\{1,3,5,9,15,45\right\}$$
Factors of $$50$$: $$\left\{1,2,5,10,25,50\right\}$$
Now list out the common factors of $$30$$, $$45$$, and $$50$$: $$\left\{1,5\right\}$$
Now, we have to choose the greatest number in the common factors of $$30$$, $$45$$, and $$50$$ which is $$5$$.
Hence, the greatest common factor of $$30$$, $$45$$, and $$50$$ is $$5$$.

Note: While splitting the middle term be careful. Factorise all the terms separately, so that you don’t miss any term of the solution. We can check if the solution or Greatest common factor divides the both original numbers completely. We can also solve this question by two more methods i.e., prime factorization and division method.