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Find the HCF of \[75\] and$15$.
A)$12$ B) $13$ C) $14$ D) $15$

Answer Verified Verified
Hint: We can find the HCF (highest common factor) by using factorization method. First, find the factors of \[75\] and $15$ respectively. Factors are the numbers that can divide the given number completely (no remainder is left). Then find the common factors from the factors of \[75\] and $15$.Find the highest number from the common factors and you’ll have the highest common factor.

Complete step by step answer:

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 correct answer is ‘D’.

Note: We can also find HCF of any number by using the prime factorization method. In this method, we find prime factors of the given numbers. Prime factors are the factors that can only be divided by 1 and the number itself. After finding prime factors, we can find the common prime factors and multiply them. The result is the HCF of given numbers. So the prime factors of the numbers will be$75 = 3 \times 5 \times 5$ and $15 = 5 \times 3$ . The common factors are $5 \times 3 = 15$. So HCF is the obtained number