Question

What is the greatest common factor (GCF) of 25 and 35?

Answer 1

Hint: In this kind of question, we need to know the basic concepts of greatest common factor(GCF), using the concept of prime factorization method, first we will find the prime factorization of 25 and 35. After that we again calculate the factors of 25 and 35 and find the greatest common factor number.

Complete step by step solution:
Greatest common factor(GCF): The largest positive integer that divides equally into all numbers with zero remainder is the greatest common factor (GCF, GCD, or HCF) of a set of whole numbers.
We have been given numbers as 25 and 35.
Let us find the prime factorization of 25. We know that the prime factor of 25 is 5.
In exponential form, we can write the prime factorization of 25 as:
$25=5^2$
Next, we will find the prime factorization of 35. We know that the prime factors of 35 are 5 and 7.
In exponential form, we can write the prime factorization of 35 as
$35=5^1{.7}^1$
Now, we will consider the prime factors of 25 and 35. The factors of any number should be dividing the given number without any remainder.
We know that the set of positive prime factors of 25 which divides 25 without leaving a remainder are (1,5).
Now, we also know that the set of positive prime factors of 35 which divides 35 without leaving a remainder are (1, 5, 7).
From the factors and prime factorization of 35 and 25, we get that the biggest common factor number is GCF number.
So, the greatest common factor of 25 and 35 is 5.

Note: Greatest common factor (GCF) is also known as highest common factor(HCF). Students may get confused about the different names of GCF, LCM, GCD and HCF. They must have basic knowledge on these. We can also use a long division method for finding GCF.