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HCF of 132, 156 and 192 is x, HCF of 105, 150 and 210 is y, and HCF of 112, 196 and 210 is z. Which is the greatest HCF?

HCF of 132, 156 and 192 is x, HCF of 105, 150 and 210 is y, and HCF of 112, 196 and 210 is z. Which is the greatest HCF? Correct Answer y

Calculation:

HCF of 132, 156 and 192 is x

⇒ 132 = 2 × 2 × 3 × 11

⇒ 156 = 2 × 2 × 3 × 13

⇒ 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3

HCF of 132, 156 and 192 is (2 × 2 × 3) = 12

HCF of 105, 150 and 210 is y

⇒ 105 = 3 × 5 × 7

⇒ 150 = 2 × 3 × 5 × 5

⇒ 210 = 2 × 3 × 5 × 7

HCF of 105, 150 and 210 is (3 × 5) = 15

HCF of 112, 196 and 210 is z

⇒ 112 = 2 × 2 × 2 × 2 × 7

⇒ 196 = 2 × 2 × 7 × 7

⇒ 210 = 2 × 3 × 5 × 7

HCF of 112, 196 and 210 is (2 × 7) = 14

∴ The greatest HCF is y

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