Highest Common Factor of 54, 86, 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 54, 86, 84 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 54, 86, 84 is 2 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 54, 86, 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 54, 86, 84 is 2.

HCF(54, 86, 84) = 2

HCF of 54, 86, 84 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 54, 86, 84 is 2.

Highest Common Factor of 54,86,84 using Euclid's algorithm

Highest Common Factor of 54,86,84 is 2

Step 1: Since 86 > 54, we apply the division lemma to 86 and 54, to get

86 = 54 x 1 + 32

Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 32 and 54, to get

54 = 32 x 1 + 22

Step 3: We consider the new divisor 32 and the new remainder 22, and apply the division lemma to get

32 = 22 x 1 + 10

We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get

22 = 10 x 2 + 2

We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 54 and 86 is 2

Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(32,22) = HCF(54,32) = HCF(86,54) .


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

Step 1: Since 84 > 2, we apply the division lemma to 84 and 2, to get

84 = 2 x 42 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 84 is 2

Notice that 2 = HCF(84,2) .

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Frequently Asked Questions on HCF of 54, 86, 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 54, 86, 84?

Answer: HCF of 54, 86, 84 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 54, 86, 84 using Euclid's Algorithm?

Answer: For arbitrary numbers 54, 86, 84 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.