Highest Common Factor of 21, 76, 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 21, 76, 84 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 21, 76, 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 21, 76, 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 21, 76, 84 is 1.

HCF(21, 76, 84) = 1

HCF of 21, 76, 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 21, 76, 84 is 1.

Highest Common Factor of 21,76,84 using Euclid's algorithm

Highest Common Factor of 21,76,84 is 1

Step 1: Since 76 > 21, we apply the division lemma to 76 and 21, to get

76 = 21 x 3 + 13

Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 13 and 21, to get

21 = 13 x 1 + 8

Step 3: We consider the new divisor 13 and the new remainder 8, and apply the division lemma to get

13 = 8 x 1 + 5

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 21 and 76 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(76,21) .

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 21, 76, 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 21, 76, 84?

Answer: HCF of 21, 76, 84 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 21, 76, 84 using Euclid's Algorithm?

Answer: For arbitrary numbers 21, 76, 84 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.