Question

Use euclid's division algorithm to find the HCF of 36 ,128

Answer 1

Answer:

HCF of 36,128 using Euclid's division algorithm is 4.

Step-by-step explanation:

Here 128 is greater than 36

Now, consider the largest number as 'a' from the given number ie. 128 and 36 satisfy Euclid's division algorithm statement a=bq+r where 0<r<b

Step 1: Since 128>36, we apply the division lemma to 128 and 36, to get

128 = 36x3+20

Step 2: Since the reminder 36 is not equal to 0, we apply division lemma to 20 and 36, to get

36 = 20x1+16

Step 3: We consider the new divisor 20 and the new remainder 4, and apply the division lemma to get

16 = 4x4+0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 128 and 36 is 4

Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(128,36).

Therefore, HCF of 36,128 using Euclid's division algorithm is 4.

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