Question

Find HCF of 18 27 and 45 using the prime factorization method

Answer 1

Answer:

Using prime factorisation the factors of the numbers are

18 = 2×3×3

45=3×3×5  

60=2×2×3×5

Now , to find the HCF of numbers we find the common factors in the above numbers and multiply them.

3 is the only number common in all the factors of the three numbers.

HCF of 18,45 and 60 is 3.

Now to find the LCM see the figure below.

LCM  = 3×2×3×5×2 = 180.

Now the product of numbers = 18×45×60 = 48600

Product of HCF and LCM = 180×3 = 540

Product of numbers ≠ product of HCF and LCM.

Step-by-step explanation:

factors of 18 = 2×3×3

factors of 27 = 3×3×3

factors of 45 = 3×3×5

In this 3×3 is common in all the terms

So, the HCF of 18,27,45 is 3×3=9

or

  _

3 | 18 , 45 , 60

2 | 6 , 15 , 20

3 | 3 , 15 , 10

5 | 1 , 5 , 10

2 | 1 , 1 , 2

1  | 1 , 1, 1