Question

Find the hcf and lcm of 144,180and192 by using prime factorisation

Answer 1

Answer:

Factors of 144 = 2×2×2×2×3×3

Factors of 180 = 2×2×3×3×5

Factors of 192 = 2×2×2×2×2×2×3

Common factors of 144, 180, 192 = {2,2,3}

LCM (144,180,192) =

2×2×2×2×2×2×3×3×5 = 2880

So, HCF(144,180,192) = 2×2×3 = 12.

Answer 2

Answer:

HCF of the given number will be 12

Step-by-step explanation:

In context to question asked,

We have to determine the HCF

As per question,

We have,

144, 180, 192

As it is mentioned to determine the HCF by using prime factorisation method.

We know that,

• HCF of two or more number is that particular number which is the highest common factors of all the given number.

• Prime factorisation method is the method in which we convert the given number as a factors of prime numbers.

• Prime numbers are those numbers which are either divisible by 1 or itself.
• HCF of any prime number is always 1

So, converting the given number in form of prime numbers,

We will get,

$144 = 2 \times 2 \times 2 \times 3 \times 3 \times 2\\180 = 2 \times 2 \times 3 \times 3 \times 5\\192 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times3\\\HCF = 2 \times 2 \times 3 = 12\:(Common\:Number)$