Question

use eaclids division find hcf of 26 and 92 135 and 225​

Answer 1

Correct Question :

• Using Euclid's Division Find HCF of 26 and 92, 135 and 225

Given :

• 26 and 92
• 135 and 225

To Find :

• HCF using Euclid's division

Solution :

⑴ HCF of 26 and 92

⟿ a = bq + r

⟿ 96 = 26 × 3 + 14

⟿ 26 = 14 × 1 + 12

⟿ 14 = 12 × 1 + 2

⟿ 12 = 2 × 6 + 0

The Remainder has Now become 0

∴ HCF of 26 and 92 is 2

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⑵ HCF of 135 and 225

⟿ a = bq + r

⟿ 225 = 135 × 1 + 90

⟿ 135 = 90 × 1 + 45

⟿ 90 = 2 × 45 + 0

The Remainder has now become 0

∴ HCF of 135 and 225 is 45.

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More to know:

Euclid’s division algorithm : This is based on Euclid’s division lemma.

• According to this, the HCF of any two positive integers a and b, with a > b, is obtained as follows:

• Step 1 : Apply the division lemma to find q and r where a = bq + r, 0 ≤ r < b.

• Step 2 : If r = 0, the HCF is b. If r ≠ 0, apply Euclid’s lemma to b and r.

• Step 3 : Continue the process till the remainder is zero. The divisor at this stage will be HCF (a, b). Also, HCF(a, b) = HCF(b, r).

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