Question

2. Find the HCF of the following numbers by the method of prime factorization:
(iii) 360, 600, 720
(iv) 630, 1890, 2835.​

Answer 1

360-2×2×23×3×5

600-2×2×2×3×5×5

720-2×2×2×2×3×3×5

Answer 2

Step-by-step explanation:

Prime Factorize all number separately

(iii) 360 :- 5 x 72

=> 3 × 24 × 5

=> 12 × 2 × 3 × 5

=> 3 × 4 × 2 × 3 × 5

=> 2 ×2 ×2 × 3 × 3 × 5

=> 2^ 3 × 3^2 × 5

Arrange in exponential form.

600 :- 6 × 100

=> 2 × 3 × 50 × 2

=> 2 × 2 × 3 × 25 × 2

=> 2 × 2 × 2 × 3 × 5 × 5

=> 2^3 × 3 × 5^2

720 :- 72 × 10

=> 9 × 8 × 5 × 2

=> 3 × 3 × 2 × 2 × 2 × 2 × 5

=> 2^4 × 3^2 × 5

If we multiply the highest powers of these number then we can find HCF

HCF :- 2^4 × 3^2 × 5^2

=> 16 + 9 + 25

Hence HCF is 50.

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