Question

Find the greatest number that can divide \[510\] and \[425\] exactly .

Answer 1

Hint: We have to find the greatest number by which the two numbers can be exactly divided . We solve this question using the concept of prime factorisation of numbers and the concept of the Greatest Common Factors of the two numbers or simply using the concept of H.C.F. (Highest Common Factor) for the numbers . We will first split the given numbers into its prime factors and then we will find the common prime factors of the two numbers and hence find the H.C.F. of the numbers . The obtained H.C.F. would be the largest number that can divide the two numbers exactly .

Complete step-by-step answer:
Given :
The given numbers are \[510\] and \[425\] .
Let us consider that
\[a = 510\]
\[b = 425\]
Now , we have to find the H.C.F. of the new values \[a\] and \[b\] .
Splitting the numbers into its respective prime factors , we can write the numbers as :
\[a = 2 \times 3 \times 5 \times 17\]
\[b = 5 \times 5 \times 17\]
From the prime factors we can conclude that the highest common factor of the two numbers can be given as :
\[H.C.F. = 5 \times 17\]
\[H.C.F. = 85\]
Hence , from the prime factors , we conclude that the greatest number that can divide \[510\] and \[425\] exactly is \[85\] .
So, the correct answer is “\[85\]”.

Note: The highest common factor of the numbers is stated as the highest common factors of the given numbers . The factor of the numbers which is common in all the prime factors of the numbers .
Similarly , L.C.M. or the least common multiple is said to be the least common multiple of the given numbers . It is stated as the number which is the multiple of the given numbers and that to the least or we can say the first common multiple .