Question

HCF of 198 and 360 by prime factorization method​

Answer 1

Answer:

Find the prime factorization of 198

198 = 2 × 3 × 3 × 11

Find the prime factorization of 360

360 = 2 × 2 × 2 × 3 × 3 × 5

To find the gcf, multiply all the prime factors common to both numbers:

Therefore, GCF = 2 × 3 × 3

GCF = 18

Answer 2

Answer:

Using the factor tree for the prime factorization of 144,180 and 192, we have

144=2

4

×3

2

,180=2

2

×3

2

×5 and 192=2

6

×3

To find the HCF, we list the common prime factor and their smallest exponents in 144,180 and 192 as follows:

Common prime factor Least exponents

2 2

3 1

∴ HCF=2

2

×3

1

=12

To find the LCM, we list all prime factors of 144,180,192 and their greatest exponents as follows:

Prime factors of 144,180 and 192 Greatest exponents

2 6

3 2

5 1

∴ LCM=2

6

×3

2

×5

1

=64×9×5=2880