Highest Common Factor of 77, 66, 41 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 77, 66, 41 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 77, 66, 41 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 77, 66, 41 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 77, 66, 41 is 1.

HCF(77, 66, 41) = 1

HCF of 77, 66, 41 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 77, 66, 41 is 1.

Highest Common Factor of 77,66,41 using Euclid's algorithm

Highest Common Factor of 77,66,41 is 1

Step 1: Since 77 > 66, we apply the division lemma to 77 and 66, to get

77 = 66 x 1 + 11

Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 11 and 66, to get

66 = 11 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 77 and 66 is 11

Notice that 11 = HCF(66,11) = HCF(77,66) .

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

Step 1: Since 41 > 11, we apply the division lemma to 41 and 11, to get

41 = 11 x 3 + 8

Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 8 and 11, to get

11 = 8 x 1 + 3

Step 3: We consider the new divisor 8 and the new remainder 3, and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 41 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(41,11) .

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Frequently Asked Questions on HCF of 77, 66, 41 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 77, 66, 41?

Answer: HCF of 77, 66, 41 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 77, 66, 41 using Euclid's Algorithm?

Answer: For arbitrary numbers 77, 66, 41 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.