Question

Use Euclid’s Division Algorithm to find the HCF of:
(i) 135 and 225​

Answer 1

Answer:

• The HCF of 135 and 225 is 45.

Step-by-step explanation:

To Find:

• Use Euclid’s Division Algorithm to find the HCF of 135 and 225.

Euclid’s Division Algorithm:

• a = bq + r

Where,

• ‘a’ and ‘b’ are positive integers.
• q = Quotient
• r = Remainder

Finding the HCF of 135 and 225:

First dividing 225 by 135.

225 = 135 × 1 + 90

Here, Quotient = 1 and Remainder = 90

Now dividing 135 by 90.

135 = 90 × 1 + 45

Here, Quotient = 1 and Remainder = 45

Dividing 90 by 45.

90 = 45 × 2 + 0

Here, Quotient = 2 and Remainder = 0

Hence,

• The HCF of 135 and 225 is 45.

Answer 2

Answer:

Step-by-step explanation:

225 > 135

Applying the Euclid's division lemma to 225 and 135,

225 = 135 × 1 + 90

Since remainder 90 ≠ 0, apply the division lemma,

Quotient = 1 and Remainder = 90

225 = 135 × 1 + 90

Divide 135 by 90

135 = 90 × 1 + 45

Divide 90 by 45

90 = 2 × 45 + 0

90 = 2 × 45 + 0

Hence, the HCF is 45.