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# Find the HCF of the following numbers 18 and 60.

Last updated date: 09th Aug 2024
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Hint: Before attempting this question, one should have prior knowledge about the concept of HCF which is the number with the greatest values which divides every one or two numbers is named as HCF, use this information to approach the solution.

Complete step-by-step solution:
We know that HCF stands for Highest common factor which is defined as the number with the greatest values which divides every one or two numbers is named HCF there is a similar term LCM which is the smallest number which is among the multiples of the group of numbers.
Since we have to find the highest common factor between two numbers which are 18 and 60.
In order to find this, we will find the factors of both the numbers by writing the numbers as a product of prime numbers.
Since, $18 = 2 \times 3 \times 3$ and $60 = 2 \times 2 \times 3 \times 5$
Factors of number 18 are 2, 3, 3 and that of number 60 are 2, 2, 3, 5.
For the highest common factor, we will multiply the common factors which are there between numbers 18 and 60
The common factors which are there between numbers 18 and 60 are 2 and 3 only
Therefore, HCF of numbers 18 and 60 = $2 \times 3 = 6$

Note: In these types of problems, we proceed by reducing the given numbers into the multiplication of its prime factors and then picking up only those prime factors which are common to the given numbers and then multiplying those prime factors in order to obtain the HCF of the given numbers.