Question

Find the HCF of 64, 72 & 112 by using Euclid’s division lemma.​

Answer 1

Answer:

8

Step-by-step explanation:Below detailed show work will make you learn how to find HCF of 64,72,112 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(64,72,112).

Here 72 is greater than 64

Now, consider the largest number as 'a' from the given number ie., 72 and 64 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 72 > 64, we apply the division lemma to 72 and 64, to get

72 = 64 x 1 + 8

Step 2: Since the reminder 64 ≠ 0, we apply division lemma to 8 and 64, to get

64 = 8 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 64 and 72 is 8

Notice that 8 = HCF(64,8) = HCF(72,64) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Here 112 is greater than 8

Now, consider the largest number as 'a' from the given number ie., 112 and 8 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 112 > 8, we apply the division lemma to 112 and 8, to get

112 = 8 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 8 and 112 is 8

Notice that 8 = HCF(112,8) .

Therefore, HCF of 64,72,112 using Euclid's division lemma is 8.

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