Question

Find the HCF of 52 and 130.

Answer 1

Hint: We will write the prime factors of each number. Then we will make a list of factors that are common to all three numbers. The highest common factor is the product of all the common factors of the given numbers. We will multiply the common factors that we listed together to obtain the highest common factor of the given numbers.

Complete step-by-step solution:
The given numbers are 52 and 130.
First, we will find the prime factors of 52.
$2 \times 2 \times 13$
Now, we will find the prime factors of 130.
$2 \times 5 \times 13$
Now, we will make a list of the prime factors that are common in both numbers. So, the common factors from the above three factorizations are 2 and 13. We know that the highest common factor of the given numbers is the product of all the common factors of the given numbers. So, the highest common factor of 52 and 130 will be the product of 2 and 13.
$ = 2 \times 13$
$ = 26$
So, the HCF of 52 and 130 is 26.

Note: The greatest number which divides each of the two or more numbers is called HCF or Highest Common Factor. It is also called the Greatest Common Measure(GCM) and Greatest Common Divisor(GCD).
It is beneficial to write the factorizations of numbers into their prime factors explicitly. This will enable us to avoid making any minor mistakes such as repetitions or omissions of factors. We should be aware of the difference between the highest common factor and the least common multiple. The least common multiple is the number that can be divided by all the given numbers and the highest common factor is the highest number that divides all the given numbers.