Question

The H.C.F of 513,1134 and 1215

Answer 1

Solution:

In this question no method is specified to find the H.C.F so
Here we find the H.C.F by Euclid division lemma:-

a=bq+r

Here a= 1215 , b = 1134

1215>1134>513

1215=1134(1)+81

1134=81(14)+0

remainder becomes 0,the Hcf of 1134 and 1215 is 81.

Then find the Hcf of 81 and 513

513=81(6)+27

81=27(3)+0

remainder becomes 0, HCF of 513 & 81 is 27.

Hence, the HCF of 513,1134 and 1215 is 27.


By Prime factorization method

1215= 3×3×3×3×3×5= 3^5 ×5¹

1134= 3×3×3×3×2×7= 3⁴×2¹×7¹

513= 3×3×3×19= 3³× 19¹

H.C.F= 3³= 3×3×3= 27

Hence, the HCF of 513,1134 and 1215 is 27.

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Hope this will help you....

Answer 2

Given numbers are 513,1134 and 1215
We have to find the H.C.F of the given numbers.
The following steps should be taken to calculate the H.C.F of big numbers:
1. Find the prime factors of all the numbers.
2. Write the numbers as the multiplication of prime numbers.
3. Find the factors which are repeating in all the numbers and multiply them to get H.C.F.
513 = 3 x 3 x 3 x 19
1134 = 3 x 3 x 3 x 3 x 2 x 7
1215 = 3 x 3 x 3 x 3 x 3 x 5
Common factors are 3 x 3 x 3
Hence,
H.C.F = 3 x 3 x 3 = 27
Which is the required answer. Hope this will help you.
Thanks.