Question

find the H.C.F on the following three different methods 38,64,82

Answer 1

38 = 2 × 19
64 = 2 × 2 × 2 × 2 × 2 × 2
82 = 2 × 41

Common factor = 2

HCF = 2

Answer 2

Answer:

2 is the HCF of (38, 64 , 82 ) .

Step-by-step explanation:

Explanation:

Given, 38 , 64 , 82.

• HCF - The greatest number that divides each of the two or more numbers is known as the HCF, or highest common factor.

• The Greatest Common Measure (GCM) and Greatest Common Divisor are further names for HCF (GCD).

Step 1:

By prime factorization method HCF of (38, 64, 82),

Factor of 38  = 2 19

Factor of 64 = 2×2×2×2×2×2

Factor of 82 = 2 × 41

So, the  HCF of (38 , 64 , 82) is 2.

List Factoring method:

List of positive integer factors of 38 that divided 38 without  a remainder,

1 , 2, 19 , 38

Factor of 64 ,

List of positive integer factors of 38 that divided 38 without  a remainde

1 , 2, 4 , 8 , 16 , 32 , 64

Similarly ,factor of 82 ,

1, 2 , 41 , 82.

So, 2 is the  common factor  of (38 , 64 , 82 ).

By using Euclid’s division lemma:

We first divide 64 by 38

             38) 64 (1

                 - 38

                    26) 38(1

                         -26

                             12) 26( 2

                                   -24

                                     2) 12( 6

                                        - 12

                                          xx

On dividing 12 by 2 we get remainder as 0.

Now, on dividing 82 by 2 we get,

                2) 82( 4

                    -8

                       2) 2( 1

                          - 2

                           xx

Here, we see that on dividing 2 by 2 we get 0 as remainder.

So, the hcf is 2

Final answer:

Hence, the hcf of (38, 64,82) is 2

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