Page 35 - SM Class 5 Inner.cdr

Note
Remember
H.C.F. of more than one number = the product of
The greatest common divisor (factor)
common prime factors. If the number do not have
of more than one number is their any common prime factor their H.C.F. is 1.
Highest Common Factor (H.C.F)

1. H.C.F. by Prime Factorization
Steps involved in prime factorization :

1. Find the prime factors of the given numbers.
2. Now list the prime factors which are common to all.
The product of the common prime factor is the required HCF.

2 20 2 28 Example 6 : Find HCF of 20, 28 and 36.
2 36
2 10 2 14 Solution : 20 = 2 × 2 × 5 2 18
5 5 7 7 28 = 2 × 2 × 7
36 = 2 × 2 × 3 × 3 3 9
1 1
The common factor of 20, 28 and 36 is 2 (occuring 3 3
two times). 1
So, HCF of 20, 28 and 36 is 2 × 2 = 4

Example 7 : Find HCF of 24 and 36.
Solution : First find the factors of 24 and 36 using prime factorization.
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
The common factors of 24 and 36 is 2 (occuring two times) and 3
(one time).

So, HCF of 24 and 36 is 2 × 2 × 3 = 12
Example 8 : Find the HCF of 11 and 15
Solution : First find the factors of 11 and 15 using prime factorization.
11 = 1 × 11
15 = 3 × 5
From the above you can see that there is no common factor. But 1 is
always a common factor between any two numbers.
So, HCF of 11 and 15 is 1.
Note : The highest common factor (HCF) of two or more given

numbers is the highest of their common factors.

2. H.C.F. by Long Division Method
To find the H.C.F. of the given number we will follow the following steps :

1. We divide the bigger number by smaller one.
2. Divide smaller number in step 1 with remainder obtained in step 1.

3. Divide divisor of 2 step with remainder obtained in step 2.
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Mathematics In Focus - 5