Question

How do you find the GCF of $40$ and $100$?

Answer 1

Hint: GCF (Greatest common factor) is also known as the highest constant factor. HCF (Highest common multiple) is the largest or greatest factor common among the two or more given numbers. To find the HCF, we must have to find out its prime factors. Prime factorization is the process of finding which prime numbers can be multiplied together to make the original number.

Complete step by step solution:
 Prime factorization is the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are the numbers greater than $1$ and which are not the product of any two smaller natural numbers. For Example: $2,{\text{ 3, 5, 7,}}......$ $2$ is the prime number as it can have only $1$ factor. Factors are the number $1$and the number itself.
Therefore,
$40 = 4 \times 10 = 2 \times 2 \times 2 \times 5$
And $100 = 10 \times 10 = 2 \times 5 \times 2 \times 5 = 2 \times 2 \times 5 \times 5$
The common factors in all the two given numbers are $2,\;2\,{\text{and 5}}$

Hence, the HCF of $40,100{\text{ is = 2}} \times 2 \times 5{\text{ = 20}}$

Note: Prime factorisation can also be done by the factor tree method. It is the factor-tree which shows the prime factors of the composite number in the form tree. One can get different factor trees to find the same prime factorization of the same composite number. HCF (Highest common factor is also known as the greatest common factor. LCM (Least common multiple) is also known as the least common divisor.