Question

find the HCF of 48 and 120 using prime factorization method​

Answer 1

Answer:

Prime Factorization of 48

Prime factors of 48 are 2, 3. Prime factorization of 48 in exponential form is:

48 = 24 × 31

Prime Factorization of 120

Prime factors of 120 are 2, 3, 5. Prime factorization of 120 in exponential form is:

120 = 23 × 31 × 51

Factors of 48

List of positive integer factors of 48 that divides 48 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24

Factors of 120

List of positive integer factors of 120 that divides 48 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60

Greatest Common Factor

We found the factors and prime factorization of 48 and 120. The biggest common factor number is the GCF number.

So the greatest common factor 48 and 120 is 24.

Answer 2

Given:

Two numbers 48 and 120 .

To find :

The HCF of 48 and 120 using prime factorization method​.

 Solution:

Step 1 of 2:

To find the HCF , we need to find the common multiples of 48 and 120 using prime factorization method.

Factor of 48 = 2 × 2 × 2 × 2 × 3

Factor of 120 = 2 × 2 × 2 × 3 × 5

Step 2 of 2:

HCF will be the common factors of the two numbers.

So, HCF of 48 and 120 = 2 × 2 × 2 × 3

HCF of 48 and 120 = 24  

Final answer:

The HCF of 48 and 120 using prime factorization method​ is 24 .