Question

4. Using Euclid's division algorithm, find the HCF of
(i) 612 and 1314​

Answer 1

GivEn:-

• GivEn number = 612 and 1314

To find:-

• Using Euclid's division algorithm find the HCF of the given numbers.

SoluTion:-

As we know that,

According to Euclid Division lemma,

✇ a = bq + r where, 0 ≤ r ≤ b .

★ Here, We have to choose the largest number first which is 1312.

Therefore,

➟ 1314 = 612 × 2 + 90

Here, a = 1314 ; b = 2 ; r = 90

★ Similarly, Applying Euclid Division lemma we get,

➟ 612 = 90 × 6 + 72

➟ 90 = 72 × 1 + 18

➟ 72 = 18 × 4 + 0

$\dag$ Now we get, 18 as the final step and remainder as 0.

$\therefore$ So, the HCF of 612 and 1314 is 18.

━━━━━━━━━━━━━━━