Highest Common Factor of 85, 77, 84 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 85, 77, 84 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 85, 77, 84 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 85, 77, 84 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 85, 77, 84 is 1.

HCF(85, 77, 84) = 1

HCF of 85, 77, 84 using Euclid's algorithm

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

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Highest common factor (HCF) of 85, 77, 84 is 1.

Highest Common Factor of 85,77,84 using Euclid's algorithm

Highest Common Factor of 85,77,84 is 1

Step 1: Since 85 > 77, we apply the division lemma to 85 and 77, to get

85 = 77 x 1 + 8

Step 2: Since the reminder 77 ≠ 0, we apply division lemma to 8 and 77, to get

77 = 8 x 9 + 5

Step 3: We consider the new divisor 8 and the new remainder 5, and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 85 and 77 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(77,8) = HCF(85,77) .

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

Step 1: Since 84 > 1, we apply the division lemma to 84 and 1, to get

84 = 1 x 84 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 84 is 1

Notice that 1 = HCF(84,1) .

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Frequently Asked Questions on HCF of 85, 77, 84 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 85, 77, 84?

Answer: HCF of 85, 77, 84 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 85, 77, 84 using Euclid's Algorithm?

Answer: For arbitrary numbers 85, 77, 84 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.