Question

Find the HCF and LCM of \[2923\]&\[3239\].

Answer 1

Hint: H.C.F. stands for Highest Common Factor also known as G.C.F. - greatest common factor. It means the greatest factor available in two or more given natural numbers. L.C.M. stands for Least Common Multiple also known as L.C.D. - Least Common Divisor. It means the lowest number which is exactly divisible by two or more given natural numbers. Commonly, there are two methods to calculate H.C.F. and L.C.M.- (i) Prime factorization method, and (ii) Long Division Method
We will use the Prime factorization method to solve the given question. At first, we will factorize two given numbers and then, we will pick up the common factors. And then, the product of all common factors will be H.C.F. and then, L.C.M. will be the product of H.C.F. and all the remaining factors.

Complete step-by-step answer:
Given two numbers are\[2923\]&\[3239\]
Let us first write all the prime factors of two given numbers, \[2923\],\[3239\]
\[
  2923 = 37 \times 79 \\
  3239 = 41 \times 79 \\
 \]
The common factor is \[79\]
Hence, the H.C.F. of \[2923\]&\[3239\]is\[79\].
And, L.C.M. of \[2923\]&\[3239\]=\[79 \times 37 \times 41\]
\[ \Rightarrow L.C.M.\left( {2923,3239} \right) = 1,19,843\]
Answer- HCF and LCM of \[2923\] & \[3239\] is \[79\]&\[1,19,843\] respectively.

Note: HCF of two or more numbers, in any case, can never be greater than any of the given numbers.
LCM of two or more numbers, in any case, can never be lesser than any of the given numbers.
There is an interesting relation between HCF & LCM i.e. \[HCF \times LCM\]= product of the numbers.
In case of co-prime numbers, HCF will always be equal to 1 and hence, LCM will always be equal to the product of given numbers.