Question

7. a) find the prime factorisaton of the following numbers in index notation. i) 12 ii) 144 iii)5040 b) the HCF and LCM of two numbers are 12 and 5040 respectively. If one of the numbers is 144, find the other number.

Answer 1

Step-by-step explanation:

i) 12=3×2×2

ii) 144=3×2×2×3×2×2

iii)5040=2×2×2×2×5×3×3×7

Answer 2

Answer:

$420$

Step-by-step explanation:

Solution:

Let the other number be x.

As we know that

★ Product of two numbers = (HCF)(LCM) ★

A/q

HCF = 12

LCM = 5040

One number = x

⟹ x × 144 = 12 × 5040

⟹ 144x = 60480

⟹ x = 60480/144

⟹ x = 420

Hence, the other number is x = 420

________________________

★ Verification ★

➟ Product of two numbers = HCF × LCM

➟ 420 × 144 = 12 × 5040

➟ 60,480 = 60,480