Question

The numbers $525$ and $3000$ are both divisible only by $3,5,15,25$ and $75$ . What is HCF $\left( 525,3000 \right)$ ?

Answer 1

Hint: Since HCF means the highest common factor, we have to find out the largest common factor of the two given numbers. In the given list of factors, as the list is arranged in ascending order, we have to pick the rightmost factor which is $75$ . This is our HCF.

Complete step by step solution:
The full form of HCF is Highest Common Factor or HCF expands into Highest Common Factor. The term factor means a number which exactly divides another number, such as $2$ is a factor of $10$ and so on. In general, there exist many factors of a number, for example $10$ has $10,5,2,1$ as its factors and so on. Now, if we consider two or more than two numbers, then they will always have a factor in common which is $1$ . In fact, it is the lowest common factor of the numbers under study. Thus, knowing the lowest common factor of some numbers is of no use as it always turns out to be $1$ . If they have other factors in common, then we need to check them. We jot down the common factors of the numbers under study. We then arrange the factors in ascending or descending order as per our convenience. After that, we select the largest of the common factors. This will be the HCF of the numbers under study.
The numbers that we have are $525$ and $3000$ . It is also given that their common factors are $3,5,15,25$ and $75$ , and they are in ascending order. The largest is $75$

Therefore, we can conclude that HCF $\left( 525,3000 \right)$ is $75$ .

Note: HCF and LCM problems are pretty easy but, there are still chances of errors. We should always check if there is any larger factor available or not. We can also solve the HCF problem by prime factorisation the two numbers and see which and how many prime factors are in common.