Question

prime factor of 72,90,180 find the HCF of 72 90 180 by prime factorization method​

Answer 1

Answer:

I know the Answer

Step-by-step explanation:

Solution:

The relation between the LCM and HCF of 72, 108 and 180 is given as, HCF(72, 108, 180) = [(72 × 108 × 180) × LCM(72, 108, 180)]/[LCM(72, 108) × LCM (108, 180) × LCM(72, 180)]

⇒ Prime factorization of 72, 108 and 180:

■ 72 = 2 × 2 × 2 × 3 × 3

■ 108 = 2 × 2 × 3 × 3 × 3

■ 180 = 2 × 2 × 3 × 3 × 5

∴ LCM of (72, 108), (108, 180), (72, 180), and (72, 108, 180) is 216, 540, 360, and 1080 respectively.

Now, LHS = HCF(72, 108, 180) = 36.

And, RHS = [(72 × 108 × 180) × LCM(72, 108, 180)]/[LCM(72, 108) × LCM (108, 180) × LCM(72, 180)] = [(1399680) × 1080]/[216 × 540 × 360]

LHS = RHS = 36.

Hence verified.

Answer 2

Answer:

prime factor of 72 = 2*2*2*3*3

prime factor of 90 = 2*3*3*5

prime factor of 180 = 2*2*3*3*5

common factor = 18