Question

Find the common factors of 72 and 75.

Answer 1

Hint: In this type of question, first find the prime factorization of the given numbers. After finding the prime factorization, find all the factors of the first number. Similarly, find all the factors of the second number then write down the common factors.

Complete step-by-step answer:
The given numbers are 72 and 75.
First of all we will write the given numbers in product form as given below:
We can write 72 in product form as:
$72 = 2 \times 2 \times 2 \times 3 \times 3$
And we can write 75 in product form as:
$75 = 3 \times 5 \times 5$

Now, from the prime factorization, we can write the factors of the two numbers which are given as:
Factors of 72 are $1,2,3,4,6,8,9,12,18,24,36,72$ .
Factors of 75 are $1,3,5,15,25,75$.
So, the factors which are common to both of the given numbers are 1 and 3.
Therefore, the common factors are 1 and 3.

Note: In this type of question, the important step is to find the factors for the given number. For finding the factors, we will calculate the prime factors of the given numbers and then calculate the factors. The factors which are common to both numbers will give the solution for the question. Another important thing is that the highest common factor will give the HCF of the given numbers.