find the HCF of the following numbers using prime factorization method 16 and 36,24 and 54. step by step explanation
Answers
Answer:
Step-by-step explanation:
We will discuss here about the method of h.c.f. (highest common factor).
Let us consider two numbers 16 and 24.
Factor of 16 are → 1, 2, 4, 8, 16
Factor of 24 are → 1, 2, 3, 4, 6, 8, 12, 16
1 × 16, 2 × 8, 4 × 4
1 × 24, 2 × 12, 3 × 8, 4 × 6
We see that the highest common factor of 16 and 24 is 8. In short, the Highest Common Factor is expressed as H.C.F.
Finding H.C.F.
There are three methods of finding H.C.F. of two or more numbers.
1. Factorization Method
2. Prime Factorization Method
3. Division Method
1. H.C.F. by factorization method
Let us consider an example.
Find the H.C.F. of 36 and 45.
Factor of 36 are →
1, 2, 3, 4, 6, 9, 12, 18, 36
Factor of 45 are → 1, 3, 5, 9, 15, 45
1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6
1 × 45, 3 × 15, 5 × 9
2. H.C.F. by prime factorization method
Let us consider an example.
Find the H.C.F. of 24, 36 and 48.
First we find the prime factors of 24, 36 and 48.
Method of H.C.F.
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
48 = 2 × 2 × 2 × 2 × 3
The common prime factors = 2, 2, 3
H.C.F. = 2 × 2 × 3 = 12
3. H.C.F. by division method
Let us consider a few examples.
1. Find the H.C.F. of 12 and 18.
H.C.F. by Division Method
Step I: Treat the smallest number i.e., 12 as divisor and the bigger number i.e., 18 as dividend.
Step II: The remainder 6 becomes the divisor and the divisor 12 becomes the dividend.
Step III: Repeat this process till the remainder becomes zero. The last divisor is the H.C.F.
2. Find the H.C.F. of 16, 18 and 24.
Highest Common Factor by Division Method
Step I: First we consider the first two numbers and follow the same step 1, 2 and 3 of the above example.
Step II: The H.C.F. of the first two numbers which is 2 becomes the divisor and the third number 24 becomes the dividend. This process is repeated till the remainder becomes 0. H.C.F. is the last divisor.
Answer:
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