Find H.C.F by using prime factor method 66 and 88.
A) 21
B) 23
C) 24
D) 22

Hint:
We are given two numbers to find the HCF of them. Prime factor method uses prime numbers. We can write the given number as a product of the prime numbers.

Complete step by step solution:
Very first we will use the prime factor method.
For 66:

For 88

Now prime factors of:
66 = \[2 \times 3 \times 11\]
88 = \[2 \times 2 \times 2 \times 11\]
Now sort the common factors of the above.
We can see 2 and 11 are common factors
Thus H.C.F . is the product of common factors.
H.C.F.= \[2 \times 11\]=\[22\]

Thus, option D is correct.

Additional information:
1) H.C.F. is the highest common factor.
2) Prime factorization is the method used to find the H.C.F. of numbers.
3) In this method, the number is broken down or is expressed in the form of the product of prime numbers only.
4) There are two methods involved in the prime factorization
4.1) Division method
4.2) Factor tree method.
5) we first find the product in the form of prime numbers.
6) Then take the common numbers and at last, find the product of these common numbers and is expressed as H.C.F.

Note:
Prime factorization is the method used to find the H.C.F. of numbers. In this method the number is broken down or is expressed in the form of a product of prime numbers only.
There are two methods involved in prime factorization.
1) Division method
2) Factor tree method.