Question

HCF of 36, 54, 60
What is the HCF of 36, 54, 60​

Answer 1

Answer: it is 6

Step 1: Since 54 > 36, we apply the division lemma to 54 and 36, to get

54 = 36 x 1 + 18

Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 18 and 36, to get

36 = 18 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 36 and 54 is 18

Notice that 18 = HCF(36,18) = HCF(54,36) .

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

Here 60 is greater than 18

Now, consider the largest number as 'a' from the given number ie., 60 and 18 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 60 > 18, we apply the division lemma to 60 and 18, to get

60 = 18 x 3 + 6

Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 6 and 18, to get

18 = 6 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 18 and 60 is 6

Notice that 6 = HCF(18,6) = HCF(60,18) .

Therefore, HCF of 36,54,60 using Euclid's division lemma is 6.

Answer 2

HI THERE THIS IS YOUR ANSWER ☺️

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to find the answer

36 : 3×3×2×2

36 : 3×3×2×2 54 : 3×3×3×2

36 : 3×3×2×2 54 : 3×3×3×260 : 2×2×3×5

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HCF : 3×2 = 6

hence 6 is the HCF of 36 , 54 , 60

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