Question

Using Euclid's algorithm find the H.C.F of 135 and 225.​

Answer 1

Answer:

135 and 225

225 is greater than 135

Therefore,

According to Euclid division algorithm

$225 = 135 \times 1 + 90 \\ 135 = 90 \times 1 + 45 \\ 90 = 45 \times 2 + 0 \\ hcm \: of \: 135 \: and \: 225 \: is \: 45$

Answer 2

Answer:

$\large \text{45}$

Step-by-step explanation:

$\large \text{we have to find HCF OF 125 AND 225 by using }\\\\\\\large \text{ Euclid division algorithm}\\\\\\\Large \text{we know that for any positive integers lemma exists as}$

Euclid's Division Lemma:

It state that two positive integers a and b exist with satisfing a  unique relation a= bq + r

where  0 ≤ r ≤ b.

$\large \text{225=135*1+90}\\\\\\\large \text{135=90*1+45}\\\\\\\large \text{90=45*2+0}\\\\\\\large \text{b=45}\\\\\\\large \text{So HCF of (135 and 225) is \boxed{45}}$

Euclid's Division Lemma:

It is use to find the Highest common factor of two or more numbers.

Lemma is nothing but proven statement which is use to prove other statement or theroem.