## Q8) Find the HCF and LCM for each set of numbers by using the prime factorization method. c) 270,330 ​

Question

Q8) Find the HCF and LCM for each set of numbers by using the
prime factorization method.
c) 270,330

in progress 0
2 months 2021-08-13T05:01:10+00:00 1 Answer 0 views 0

### HCF = 30

Step-by-step explanation:

## LCM

Prime Factorization of 270 is:

2 x 3 x 3 x 3 x 5 => 2^1 x 3^3 x 5^1

Prime Factorization of 330 is:

2 x 3 x 5 x 11 => 2^1 x 3^1 x 5^1 x 11^1

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 3, 3, 3, 5, 11

Multiply these factors together to find the LCM.

LCM = 2 x 3 x 3 x 3 x 5 x 11 = 2970

In exponential form:

LCM = 2^1 x 3^3 x 5^1 x 11^1 = 2970

LCM = 2970

Therefore,

LCM(270, 330) = 2970

## HCF

HCF = 30

for the values 270, 330

Solution by Factorization:

The factors of 270 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270

The factors of 330 are: 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330

Then the greatest common factor is 30.