Question

Find the HCF of 135 and 345 using Euclid’s

division algorithem​

Answer 1

Answer:

HCF(135, 345) is 15.

Step-by-step explanation:

Given two numbers are,

135 and 345

To find,

Highest Common Factor (HCF) = ?

By using Euclid's division algorithm,

Since 345 > 135, we've to divide 345 by 135.

By using Euclid's division lemma,

345 = 135 * 2 + 75

Since, r ≠ 0, we've to divide 135 by 75 to get,

By using Euclid's division lemma,

135 = 75 * 1 + 60

Since r ≠ 0, we've to divide 75 by 60 to get,

By using Euclid's division lemma,

75 = 60 * 1 + 15

Since, r ≠ 0, we've to divide 60 by 15 to get,

By using Euclid's division lemma,

60 = 15 * 4 + 0

Since, r = 0, the divisor of the last step will be the divisor of the given two numbers.

Therefore, 15 is the HCF of 135 and 345.

$\boxed{\large{\bold{Note:}}}$

Lemma :

A proven statement which is used to prove another statement.

Algorithm :

Step-by-step process to solve any problem.

You can't write the answer directly. You've to write it with full steps.