Questions & Answers

Question

Answers

A)$12$ B) $13$ C) $14$ D) $15$

Answer
Verified

Here, given numbers are\[75\] and$15$. We have to find the HCF (highest common factor) of these numbers. We can use factorization method to find the HCF of these numbers. First let us find the factors of both the numbers. Factors are the numbers which can divide the given number completely (no remainder is left).Now we know that \[75\] is a composite number as it has more than two factors. So we can write $75 = 3 \times 25$$ = 3 \times 5 \times 5$ or as $75 = 15 \times 5$ or $75 = 75 \times 1$.These are all factors of the number \[75\] .Now we can write $15$ as $15 = 15 \times 1 = 5 \times 3 \times 1$. So we can write-

Factors of \[75\]$ = 1,3,5,15,25,75$ and Factors of $15 = 1,3,5,15$

So here we can see that $1,3,5{\text{ and 15}}$ are the common factors of \[75\] and $15$. In these common factors, $15$ is the highest factor. So we can say that the highest common factor of these numbers is $15$.

Hence the